I am glad that you are able to recognize your limits. It is better for your mom in the long run if you wait until you can care for her/someone can. Also, keep in mind that a home health aide or someone similar might could assist you with caring for her. My step-father was released from the hospital a while back and has someone come over to do physical therapy on at least a weekly bases. They also waited until he could get up with little help because my mom can't be expected to lift him up. I suspect that they will give you a chance to assist her some at the hospital to see if you can do it and to teach you how to care for her. Hopefully, they would also help you to find other sources of help. It is very hard for anyone to become a caregiver for another. Therefore it is important for the caregiver to get support for him/herself too. I hope you do that.
If you can't handle caring for your mom, assisted living which is not quite a nursing home might be an option. Otherwise, you could probably talk to the hospital's social worker. They will hopefully work with you to find a solution for you and her.
Good luck. I hope things work out for you.