John 14:12-14 says,
"12 Verily, verily, I say unto you, He that believeth on me, the works that I do shall he do also; and greater works than these shall he do; because I go unto my Father.
13 And whatsoever ye shall ask in my name, that will I do, that the Father may be glorified in the Son.
14 If ye shall ask any thing in my name, I will do it." (KJV)
So you can pray and ask in Jesus' name and if you believe on Jesus, and His works, you can believe your prayer will be granted.
As for what this belief involves ask yourself if you believe in what Jesus stands for, what He said and did, as written in the Bible. If you do, He is in your heart.
How to believe this? Practically, believing in anything means dismissing doubts or not letting doubts overrule your thinking - thus still leaving your mind open to possibilities. Or you can face your doubts head on and examine their plausibility. Whichever you feel most comfortable with.
It sounds like you have experienced some very difficult experiences. I think you need to give yourself time to heal from them. Regarding feelings not everyone feels different immediately, it is often a process which takes time.
I hope you find a place of more calm and peace soon. 