First, if you're struggling with this you should seek out help. There are numerous mental illnesses that can result in people struggling with religious matters, such as hallucinations and delusional thinking, a form of OCD that is based on religiosity, and so on.
Please note I'm not saying that people who believe in deities are mentally ill, nor am I saying that being mentally ill is a bad thing. I've struggled with mental illness so that was in no way meant as an insult. I'm just saying that, if something is causing you distress, it's a good idea to see a professional who can help you cope.
In the light of what I said above, yes, some types of mental illness could "force" you to believe in deities you don't necessarily want to believe in. I also think it's possible to simply believe against your will without being mentally ill, but if they're ones you've made up and it's starting to be harmful to you, then it sounds like mental illness could be at work here.
I don't think that any God or Gods would ever be offended by someone with a mental illness. If you're being forced by your illness to believe in gods you've made up in your head and you don't want to believe in them, I don't think God would be offended by this. After all, God knows what you're going through so I think it's different from willingly believing in other Gods (not that I think believing in other Gods is bad either, I believe in them myself, I'm just talking in terms of ideologies within Christianity where you can only believe in and worship the Christian version of God).
I think that any deities who would be offended by your mental illness would not be very compassionate ones. After all, in most belief systems deities know what is going on with you and hear your prayers. So why wouldn't they know you're struggling with a problem?
Imagine this. You have a friend who has a mental illness. This friend does things that are not harmful to you or anyone else, but which are causing her distress. Would you be angry with this friend just because of that?
Another thing, to reply to your "I do not believe in Christ is because he promised he would never leave me and also that he would never put on me more than I could bear" is this: trouble happens because we're human. I can't think of anyone who has never gone through a rough patch. Even people who seem to be very lucky have probably dealt with problems in some way, be it the loss of a loved one or something else.
Some people think mental illness and trouble in general is simply a test put to you by God, to make you grow stronger. I personally don't believe that and think it's harmful to think that way but if it makes you feel better, you can choose to believe it.
I personally prefer to think this way: I can't think of anyone of any religion who has just had any and all problems miraculously removed from their lives because as I said, negative things can happen to everyone and it's simply a part of being human.
I'm no longer a Christian but I don't think that the fact that you've been dealing with these issues means Jesus is not on your side. Imagine you have a friend and you promise you'll support and help this friend. This means you can be this friend's source of solace and a shoulder to cry on, but you can't necessarily make his problems disappear when he runs into them.
I hope this helps. As I said, I think right now the best step to take would be to seek help, like therapy for example, to discover the root of your problem and address it in a way that works for you, whether that's some form of therapy or medication or both.
