C.S.
Hi Angel,
A home-maker is usually someone who performs maid type duties like cleaning the house, doing laundry and cooking. They are not for watching children. It sounds like a mother's helper might be a good solution for you. A mother's helper is usually a high school student who comes to "babysit" when you are home - leaving you some time to do something else. In your case, a mother's helper might be able to go with you and Jake to parks and other outings.
I looked at your other posts to see that you have been struggling with this for awhile. When you take Jake for his 3 year appt with the pediatrician, please ask them for any suggestions/ideas. Your pediatrician should know what services are available in the area. I really liked the bell idea that a previous poster gave you and hope you followed up with her. Another idea is that when you are out and about on public transport, use a child-leash. I did when my son was that age and I don't have any disabilities other than age!
NJ is known to have very good services for those with disabilities. My aunt has a son with cerebal palsy and she moved there because of all of the services available.
Best wishes, you are an inspiration! C.