You're certainly physically burnt out. I wonder why you're thinking you have to do everything yourself. Why don't you hire a babysitter? Why don't you take time for yourself?
You've received suggestions for finding a babysitter you can trust. I would also consider neighbors. Do you know them? From time to time, my daughter who lives in an apartment complex has found a friend living in the same complex. It's harder to get to know your neighbors if you live in a house and perhaps you need to wait until you're well to work on that one. I do know that I've received and given support within my neighborhood. It does take effort to get to know them.
You can have someone come in to be with your son while you do something for yourself, even if it's to just sleep. It does take time to get a routine going so that your son won't come into your room. This person can be a youngster. When my granddaughter was young, two 12 yo girls filled in as mommy's helpers. I even took one of them with me when I had to take my granddaughter shopping with me. They managed the baby while I did my things. They took her to the playground outside the apartment while I cleaned or did laundry.
You may be able to find girls this age by asking at the daycare center (older sibs) or an elementary or middle school. Spend time with them until you're comfortable trusting them to be alone with your son.
You mention having gone to mommy and me groups. Do you know why they haven't worked for you? Is it possible that because of your stress you've pushed others away? Have you gone back several times? Often it takes awhile to make a connection.
I also suggest that you're depressed and urge you to talk with your doctor about taking an anti-depressant.
Your son will be just fine with a babysitter. You need to take care of yourself so that you can take care of your son. You have to be number 1 on your list with him being a very close second. As you're seeing, you cannot be a good caretaker when you're sick.
You are teaching him to never rely on anyone but himself. Is this your choice or is it happening because of circumstances. I urge you to find out for yourself and to teach him that we have to rely on others. We can not be totally independent as it seems you're now learning. Find just one person on whom you can depend. Scary, I know. Take a leap of faith. Start with a counselor. Learn how to recognize someone that you can trust. Learn how to be trustworthy and dependable for someone other than your son.
I suggest that you're ill because you've not taken care of yourself. You've tried for too long to be totally independent and hopefully you see that being so independent is not working. Get started in counseling so that you can make your life better for yourself and your son. Let go of the anger and hurt from the past and seek love in your life.
All too often we get what we ask for. Seems you're asking to be totally independent while yearning for love. As long as we hold onto the anger and pain we will continue to get anger and pain. When we are able to love other people, love comes back to us.
I suggest you start by finding a loving, capable, reliable baby sitter for your son. They are available. And get started with counseling. Perhaps start on an anti-depressant. Expect life to get better.