Question about minimum credit card payments?

I live in FL.....I have credit cards and lines of credit and a mortgage. Everything has been fine for the last several years until May of this year. My boyfriend I bought the house with took off (house is in my name) and I have several bills I am trying to manage, and even with renting out 2 rooms in my home I am still having a hard time making ends meet. The things that can be reposessesd I pay on furniture (nothing fancy, we just didn't have anything when we bought this place), air conditioner (that broke and had to be replaced about 2 years after we moved in here...I live in Fla, can't be with out a/c). I had to have some surgery that insurance didn't entirely cover that my doctor's office had (Carecredit) a line of credit opened for me that would cover the balance (No it was not a tummy tuck or lift or anything superficial-all medically necessary) The medical lines of credit which are about $2K & 3K each I have been sending anywhere from $5.00 to $10.00 or sometimes even $1.00 amonth and then there's Chase which is another credit card, which is about $5K and that was used primarily for balance transfers and etc. So here I am, he left, I am not in the best of health, but I am working full time and just barely making my mortgage. I have been told that as long as I am even sending them a dollar a month they cannot sue me .....I plan to do this until I get the other things paid off and then I will start to pay them, I have drained all my 401Ks and to no avail. I am not trying to run from this, and no we didn't go hog wild and buy Gucci handbags and designer clothes and etc. When he bailed on me, he took his $ with him, the problem is, is that all these debts are in my name, even though somethings were for him as well like car repairs. I get about 25+ calls each day with hateful messages that "I need to call in today" I did try to call Chase and told them I can send about $10.00 for a while, they just laughed and had no options for me. I cannot afford to have my wages garnished as I have medical expenses that I need to pay for, a son to raise and a home/roof to keep over our heads. I am just sick about this....What will they do to me and is it really true as long as I send in even just a dollar a month and never miss a month that they cannot come after me? Please advise.