You need a good tutor. I suggest finding a math major at a local university to teach you.
The problem is that, from what I can infer from your description, you don't have the fundamental skills necessary to self-tech effectively. You could try using some of the resources mentioned by other commenters, but chances are this process will much more tedious than if you had a mentor, and you'll probably come to believe various incorrect things that you'll have to unlearn later. Real-time feedback and correction would be more effective.
Also, I disagree with some of the advice given here. (Suggesting resources on Coq and ZFC to someone asking how exponents work? Really?) Tread carefully, and prefer the recommendations of people who have experience teaching high school students and undergraduates.
Yes, you are right. I've taught proofs in a college setting for thirty years, both in a Discrete Math class largely for CS majors and in a Math major course (done inquiry style). People often convince themselves that they have things right when they are mistaken. Everyone does it, even the best students. OP, you should try to get someone to work with you.
> OP, you should try to get someone to work with you.
Those both sound like great suggestions to me.
When I was a linguistics major in college, around 1976, I started wondering about pure mathematics—it seemed a lot more interesting than high-school calculus, which had snuffed out my previous interest in math—so I took an introductory class in abstract algebra. It was the first math class I had taken that was oriented around proofs rather than calculation, and I had trouble at first understanding what proofs were and how I was supposed to come up with them.
I went to see the professor during his office hours to ask for advice, and he told me something like this: “A proof is basically a story you tell to other mathematicians.” It took a while for the meaning of his advice to sink in, but it did eventually, especially after I took a couple of seminar-style classes in which the students worked on proofs together.
Looking back now, I would summarize what I learned then as follows: A proof is a story you tell to other intelligent, knowledgeable people to convince them that the theorem is true. As with all story-telling, you have to adjust what you say and how you say it depending on your audience and on their knowledge and expectations. If you are new to mathematical proofs, then you need to work with other people for a while to learn how mathematicians use proofs to tell stories to each other.
The problem is that, from what I can infer from your description, you don't have the fundamental skills necessary to self-tech effectively. You could try using some of the resources mentioned by other commenters, but chances are this process will much more tedious than if you had a mentor, and you'll probably come to believe various incorrect things that you'll have to unlearn later. Real-time feedback and correction would be more effective.
Also, I disagree with some of the advice given here. (Suggesting resources on Coq and ZFC to someone asking how exponents work? Really?) Tread carefully, and prefer the recommendations of people who have experience teaching high school students and undergraduates.