How can I process guilt over the fact that my mental health is ruining my marriage?

Seek help. The guilt is there as you describe, but also may be a direct symptom of your mental health problem leading to a vicious cycle. Talk to you doctor, see a psychiatrist, try counseling as well, some therapies such as cbt work to change your thinking patterns. Certain meditative techniques can also be effective. Take action and dont process alone, .
Mental health. This usually requires professional help. Call your doctor for advise and proper treatment.
Shame/guilt. Shame is caused by many things and is experienced very differently by different people. Sometimes people have done things they probably should feel shame about, while many others have not; they only think they should feel ashamed because an authority figure has told them to. Everyone feels shame; it's the rule and not the exception. Find a reputable psychotherapist to speak with in a safe place.