There are different schools of thought on a person believing in Christ, then falling away. There are people who believe, profess faith, seek to live that life for a period of time, then due to life struggles that faith is diminished. The person may become disillusioned and "fall away" for a period of time, perhaps years. But, if the Holy Spirit dwells within that person he/she still desires a relationship with God because he/she is born of God. The Spirit within him is still crying out "Abba, Father" even if that person is not a "practicing" believer. At some point many such people return to God because they are truly His children. I don't believe they were ever lost as far as spiritual destiny and identity, only lost and confused in their own minds as to what had happened to them and trying to make sense of what had happened to them in context with their faith.
IT's not wise to accept the opinions of others over your own thoughts and opinions. I say this in regards as taking as the absolute truth what your church said about falling away after believing. You have to come to your own conclusion and opinion as to what scripture says and means.
I don't know you, Orion, but my gut tells me that you are a perfectionist, a worrier, an obsessive thinker, and that you probably have low self-esteem and probably beat yourself up on a continual basis. If this is the case, it may be theses traits, not God, causing the doubts.
Predestination is in the Bible. I wish it weren't, but it is. To say that "anyone" can believe is not scripturally accurate, in my opinion, and goes against the words of Christ in the New Testament. But, to say that you are not chosen could be a "black and white" cognitive distortion which may be the result of the traits I spoke of. That's my opinion, anyway. The fact that you have a desire to be saved or to know God or not go to hell may be the Holy Spirit's working inside of you. It also may be of the Spirit that you are here on this board and that you go to church. Have you given any thought to this that these motivations could have come from God and not from you?
FAith is not a feeling, it is a cognitive, willful choice. It is believing that God is and that He will reward you for seeking Him, simple as that, Hebrews 11:6. There was another young man who lived in the 18th century whose spiritual journey was somewhat similar to yours to a point. His name was David Brainerd. His struggles and thoughts are documented in the book, "The Life and Diary of David Brainerd" by Moody Press.
http://www.amazon.com/Life-Diary-David- ... 1428632271
To quote from this, book, on page 27 Brainerd speaks of the sovereignty of God.
"4. Another thing to which I found a great inward opposition was the sovereignty of God. I could not bear that it should be wholly at God's pleasure, to save or damn me, just as He would. That passage, Romans 9:11-23 was a constant vexation to me, especially verse 21.................It gave me such me such a dreadful view of myself that I dreaded more than ever to see myself in God's hands, at His sovereign disposal, and it made me more opposite than ever to submit to His sovereignty; for I thought God designed my damnation.
All this time the Spirit of God was powerfully at work with me;....."
As far as believing everything that is written in scripture, keep in mind that when Jesus was alive the New Testament had not been written. I would advise to seek faith in Christ, His existence and resurrection, and everything else will follow. "If anyone hears my voice and opens the door, I will come into Him". Rev. 3:20. Sounds to me like you may have already done this at some point but have become disillusioned.