While I, personally, feel like religion being interjected into these processes likely dilutes their efficacy, if you feel like it may help you to work through them, then by all means do it. If you don’t feel that way, then, again, it’s your well-being and you need to put that first. Things may be rocky, but the people who love you will adapt.
If you’re a dependent, however, and you live with them, it’s best to keep things smooth and diplomatic. Maybe strike some deal where you see a secular psychologist but also assuage her fears by agreeing to some form of religious something or other? I honestly don’t know what the best option would be, and I can’t really tell you what to say. Just be insistent but understanding and open.
I wouldn’t say you’ve made things worse, these things just need to be massaged and dealt with in a diplomatic fashion. As your mother, the hope is that she will eventually realize that your well-being is more important than her desires for your religious beliefs.
All parents eventually go through this sort of “disappointment” at some point in their parenting careers: whether their child is gay, religious, not religious, not a fan of their favourite sports team, didn’t get into their university, a Liberal Arts Major rather than a doctor, doesn’t want children, moves out of state/country, or a million other things, something you do will disappoint them and they will cope with it, come to terms with it, and hopefully move on. You must do what is best for your mental heath, whatever it may be.