Hi J.,
I actually used to work in the Academic Internal Medicine clinic at St Joe. They take the WHP, not sure if that is where you are receiving treatment or not. HOWEVER, they and most offices affiliated with the hospital have a social worker on hand that can help you get a referral to a Psychiatrist. With that being said, while I understand you feel that meds alone would not help, you may be very surprised at how they take the "edge" off of what you are going through.
I am married now, but I was a single mom with two boys for 10 years, your life is not over, and you are much much stronger than you believe you are. Women are amazing creatures, do not underestimate yourself and the power you have in you to dictate the next steps of your life. Being alone can be scary but it can also be liberating---we make the choice of which road we take. I went to Purdue, got a Bachelor Degree, raised my children, bought a house---you CAN do it alone, you CAN.
Medication may really help you get through the worst of this, and brighten those dull sad days for you. These days are days you can never get back with your kids, don't let a few weeks turn into a few months or God forbid a few years, of never feeling happy. Call your Dr and at least get on the meds and try to talk to a social worker, or see if you can get a referral to counseling. GOOD LUCK you WILL BE OK!!!