There are several aspects to this, each of which necessitate a separate answer, so bear with me.
A) How does God want Christians to feel inside?
- A Christian has an obligation to walk by the Spirit and not according to the flesh.
"So then, brethren, we are under obligation, not to the flesh, to live according to the flesh- for if you are living according to the flesh, you must die; but if by the Spirit you are putting to death the deeds of the body, you will live." (Romans 8:12-14, NASB)
"But I say, walk by the Spirit, and you will not carry out the desire of the flesh. For the flesh sets its desire against the Spirit, and the Spirit against the flesh; for these are in opposition to one another, so that you may not do the things that you please." (Galatians 5:16-17, NASB)
"Now those who belong to Christ Jesus have crucified the flesh with its passions and desires. If we live by the Spirit, let us also walk by the Spirit." (Galatians 5:24-25, NASB)
- Walking by the Spirit results in "the fruit of the Spirit", while walking according to the flesh results in "the deeds of the flesh." (Although these are mostly external expressions, it is easy to see that they are connected to internal feelings.)
"Now the deeds of the flesh are evident, which are immorality, impurity, sensuality, idolatry, sorcery, enmities, strife, jealousy, outbursts of anger, disputes, dissensions, factions, envying, drunkenness, carousing, and things like these, of which I forewarn you , just as I have forewarned you, that those who practice such things will not inherit the kingdom of God. But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control; against such things there is no law." (Galatians 5:19-23, NASB)
- The "fleshly feelings" can be pretty concisely and accurately summarized as "lust and pride", or just "selfishness." Ideally we would not feel these things.
"For all that is in the world, the lust of the flesh and the lust of the eyes and the boastful pride of life, is not from the Father, but is from the world. The world is passing away, and also its lusts; but the one who does the will of God lives forever." (1 John 2:16-17, NASB)
"Do nothing from selfishness..." (from Philippians 2:3, NASB)
"and He died for all, so that they who live might no longer live for themselves, but for Him..." (from 2 Corinthians 5:15, NASB)
"I have been crucified with Christ; and it is no longer I who live, but Christ lives in me..." (from Galatians 2:20, NASB)
- So, the first part to the answer is that ideally a Christian would not feel things like lust or envy, for instance, but would feel things like peace and joy.
- In heaven, God has emotions
"The Lord was sorry that He had made man on the earth, and He was grieved in His heart." (Genesis 6:6, NASB)
"...The Lord scoffs at them... He will speak to them in His anger, And terrify them in His fury..." (from Psalm 2:4-5, NASB)
"The LORD your God ... will exult over you with joy, He will be quiet in His love, He will rejoice over you with shouts of joy." (from Zephaniah 3:17, NASB)
- On earth, Jesus had emotions.
"Jesus wept." (John 11:35, NASB)
"And Jesus called His disciples to Him, and said, 'I feel compassion for the people, because they have remained with Me now three days and have nothing to eat; and I do not want to send them away hungry, for they might faint on the way.'" (Matthew 15:32, NASB)
"And Jesus answered and said, “You unbelieving and perverted generation, how long shall I be with you? How long shall I put up with you?" (from Matthew 17:17, NASB)
- Man was made in the image of God, and one of the aspects to this is that we have emotions, just like He does.
"Be angry, and yet do not sin..." (from Ephesians 4:26, NASB)
"...you shall rejoice before the LORD your God..." (from Deuteronomy 12:12, NASB)
- The capacity for emotion comes from God and is good. However, a given emotion may be appropriate in one situation, but inappropriate in another.
"[Love] does not rejoice in unrighteousness, but rejoices with the truth" (1 Corinthians 13:6, NASB)
"...the LORD loves the sons of Israel, though they turn to other gods and love raisin cakes." (from Hosea 3:1, NASB)
- So, the second part to the answer is that Christians should feel free to experience their God-given emotions (as long as it is not inappropriate or controlling.)
B) If a person is truly a Christian, how will they feel inside?
- It is important to understand that while God desires for His people to experience the fruit of the Spirit and appropriate emotions, every Christian deviates from this to some degree.
"...I joyfully concur with the law of God in the inner man, but I see a different law in the members of my body, waging war against the law of my mind... So then, on the one hand I myself with my mind am serving the law of God, but on the other, with my flesh the law of sin." (from Romans 7:22-25, NASB)
"For we all stumble in many ways..." (from James 3:2, NASB)
"If we say that we have no sin, we are deceiving ourselves and the truth is not in us." (1 John 1:8, NASB)
(See also Rom 14:23, Jas 4:17, Matt 5:45, etc.)
- So, the third part to the answer is that it is possible for a Christian to feel pretty much anything.
C) How do Christians feel about God's deliverance?
- As we have seen, it is OK for a Christian to feel emotions. In a given situation, one Christian may feel anger, while another may feel pity - and hypothetically, they could both be perfectly acceptable to the Lord. It is interesting to look at how the people of God have historically responded to difficult times and God's promise of deliverance.
"Be gracious to me, O LORD, for I am in distress; My eye is wasted away from grief, my soul and my body also. For my life is spent with sorrow And my years with sighing" (Psalm 31:9-10, NASB)
"Though He slay me, I will hope in Him. Nevertheless I will argue my ways before Him." (Job 13:15, NASB)
"...there they crucified Him... But Jesus was saying, 'Father, forgive them; for they do not know what they are doing.'" (from Luke 23:33-34, NASB)
- Aside from emotions, there are some common themes throughout Scripture that relate to this question - this world is corrupt, it is a difficult place for the people of God, He will fix it, and we can look forward to that.
"For we know that the whole creation groans..." (from Romans 8:22, NASB)
"Indeed, all who desire to live godly in Christ Jesus will be persecuted." (2 Timothy 3:12, NASB)
"All these died in faith, without receiving the promises, but having seen them and having welcomed them from a distance, and having confessed that they were strangers and exiles on the earth. For those who say such things make it clear that they are seeking a country of their own... a better country, that is, a heavenly one. Therefore God is not ashamed to be called their God; for He has prepared a city for them."
"Then I saw a new heaven and a new earth; for the first heaven and the first earth passed away... And I heard a loud voice from the throne, saying, '...God Himself will be among them, and He will wipe away every tear from their eyes; and there will no longer be any death; there will no longer be any mourning, or crying, or pain; the first things have passed away.'" (from Revelation 21:1-4, NASB)
- So, the fourth part to the answer is that believers are indeed afflicted in many ways, and the Lord will indeed deliver us, and it is good to look forward to this.