Will he give me a second chance?

Give him space. Let him figure himself out. It sounds like he still has feelings for you but he doesn't know what to do. So give him space. Don't contact him for awhile. For now, focus on your son. And yourself. YOu said you have a mental illness. SO try focusing on how to make things better for you and your son. You and your son can't continue relying on your ex anymore. You have to learn to live without him, for now at least. Right now, he doesn't want to totally lose you. That's why he doesn't respond. But he also dosnt know if he wants to be wtih you. He's confused.
Just give him time. Don't bug him, text, email, or call. Just let things be.
If he decides he wants to be there for you during this illness, and wants to work things out, then he will come back, voluntarily. But if he doesnt, then, you know what that means.
Iv read your other question about him, and trust me, he won't come back by you (sorta) begging him back.
Would you really want to be with someone who gives up or runs away when things get rough? You need someone right now, due to your condition, and he knows that, but -- where is he?
Just let him go for now. Focus on your family. And things will fall into place. Everything will be ok.
Sometimes when you hold on too tight, it just pushes the other person away. So let go, and just trust that everything will fall into where its supposed to.

Yes he will give a second chance if you ask him out again.

what was the damage? the worst that can happen is that you cheated on him?

There is always a chance. I would ask him if he would consider being friends and maybe working back up to having a relationship again. I would also sit him down and tell him a little more about the illness you have.