That is actually one of the main attacks of Satan, especially during the first two years in the faith. I also fought with that doubt in my mind: "Am I a Christian? Am I one of the chosen ones?" I came to the conclussion that what I was doing was focusing more on my own reasoning and actions, rather than on God's Word. If He has said that those who believe in Him have eternal life, then it's true. God can't lie, and the reason why He sent His Son to die in the cross was precisely to give us eternal life (John 3:16), and to reconcile us with Him (2 Cor. 5:20).
We might not feel His presence for hours... days... weeks... months... and some Christians have been like this for years, yet the calling is for obedience, not for living our way because we don't feel His presence. Those were hard days... it was difficult for me to read the Bible or pray without feeling God's presence, but after I understood that obedience and faith in His Word played an important role more than my changing feelings, I continued doing those "spiritual exercises," as someone called them.
The situation is often called or described as "spiritual dryness," and its causes can be one or more of the following:
1) Physical weariness (or laziness).
2) Leaning to worldly habits or conforming to worldly patterns.
3) The end of a ministry where you were intensely participating (this was my case, as I used to lead prayer groups and chapel in my school. After I left school, I started having those spiritual dryness times). Or having a "break" after strong spiritual work.
4) Sin (unconfessed sin, or indulging sin).
5) Other causes.
I suggest holding to God's promises. Trust Him with all your heart, and soul, and mind. Keep on reading the Scriptures. Don't neglect going to church and meeting with other believers. And don't... I repeat, don't, forget to pray: Tell God your feelings about this condition, and ask them if it's His will to take you out of it so you can rejoice in Him once again. Keep your hope, and don't dismay.
Galatians 6:9
Let us not become weary in doing good, for at the proper time we will reap a harvest if we do not give up.