Gud,
Consider:
The infection in your leg, whatever the cause, required professional treatment to resolve, and you got that.
Having thoughts along the lines of "I'm a shitty person," whatever the cause, also requires professional treatment to resolve. Get that.
The one is no less dangerous than the other.
Gud, crazed killers have fulfilling relationships. You are more than able to have a good one with someone who loves you back.
My wife is a good person
Nope. Although, I don't know her, so I guess I can't really say.
But she is not acting like a good person. If she makes you feel this way, then she should know something is wrong, and she should want to fix it. If you want to go to therapy, for example, she should support you, even if she's not willing to attend herself.
She can be mad at you, but she cannot behave in a way that makes you believe you're worthless or broken.
Gud. I do not for one moment think you are a shitty person. What's more, being diagnosed on the spectrum does not make you defective. I'm deaf in one ear. Sometimes people have to work a little harder to get my attention so I answer their questions or do something they would like me to do. Does that make me defective? Shitty? A bad person who doesn't deserve to have loving, respectful relationships with the people close to me? I hope not.
Gud, regardless of your wife's intent or what she says to you, thinking the way you do about yourself just isn't good. I try not to comment directly about your wife because I know from personal experience it is possible to feel horrible about yourself and put thoughts on what other people think about us without any intent on their part. This doesn't have to be about your wife but about what you need to start feeling better about yourself.
I'm just not good enough.
As she constantly makes you believe this, she is NOT a good person. Certainly not toward you. You deserve better.
YOU. ARE. NOT. DEFECTIVE.
(Sorry for the shout. But.)
I don't know about therapy. I feel like I'd have to do it in secret which is hard on my schedule and money really is tight right now
Again, there are places that do sliding-scale payments. And check your insurance -- the copay might be lower than you think. (Mine is $25. I was really surprised at that. And thrilled, because it means that weekly therapy doesn't break the bank.)
I've been diagnosed with Asperger's twice independently, so I know I'm defective
You're not defective. Being on the spectrum doesn't make anyone defective. Ever. It doesn't make you unable to love someone. It doesn't make you unworthy of love.
I hate my wife coming across as a bad person because of my problems.
She doesn't come across as a bad person because of you; she comes across as a bad person because she is abusing you.