Congrats on the Baby!!!
You do have some options here. I agree with the other posters that you should let your family know what is going on. I am not sure what their financial situation is - hopefully, they can help you out.
If they cannot, I advise that you apply at your state medicaid office immediately. Pregnant woman are moved to the top of the line. You should be able to get state assistance which might include paying for your utilities. You will also get help with the baby including health insurance, formula, diapers etc.
As for him - yes you should sever ties with him. He isn't clean. This is just one disappointment after another waiting to happen. Focus on your child and his upcoming birth and protecting both of you since there is no income coming in.
Its very easy for me to say cut ties, I don't walk in your shoes. I do have a lot of compassion for the situation you are in. Rely on your Mom and Sister right now for emotional support I am sure they will give it to you.