A few comments that I hope can help:

1) It's OK to believe simply because your heart tells you to. Belief in God, so say the Christian philosophers, is properly basic. ie. it's a type of belief that doesn't require outside justification to be justifiably held to. This is the internal testimony of the conscience that is part of general revelation.

2) That being said there are copious amounts of external, rational evidences that you can use to convince your intellect that the God exists, Christ is God and the Scriptures are reliable. This is called apologetics and I've always said that the greatest value of apologetics is to strengthen christians. I strongly advocate you pick up some apologetic resources. You can find the stuff all over the web as well as in good books. They range in content from philosophical to historical to scientific. After delving deeply in to apologetics I now only have the vaguest moments of existential doubt which my mind can quickly bannish as I go over the evidences in my head.

3) don't knock yourself out too much over your doubt. Your salvation is not on the line here. Your salvation depends on Christ alone, it's not even your responsibility to maintain your faith, He sustains that too. True, there will be those who are cast out..."depart from me, I knew you not". But if you read the context you will see that those are "doers of iniquity" They are people who lived licentiously. Perhaps included are those who hold heretical views of Christ. I sincerely doubt that any of those people were agonizing over whether they were saved prior to meeting Christ first-hand.

4) Perhaps much of your doubt comes because you have been taught all your life by our culture that Christianity is irrational and that science has proven that so. That it's an ancient mythology for the weak-minded. If so, go back to suggestion #2 and you'll see that's a totally false position.

5) I want to warn you against thinking that the strength of your faith is what secures your salvation. I also want you to know that the solution to intellectual doubts is to seek to understand the intellectual basis for the truthfulness of Christianity. (again back to point #2)
Keep in mind that 'Faith' is not simple belief or an act of the will. But rather it's 'trust' grounded in objectively known facts.

So study up.