Have I done the right thing? I need help/advice.

I got my cat Tigger from a pregnant neighbour a few months ago. He was my first pet cat and he was the best cat I could have ever hoped for. A few weeks ago I noticed him acting more lethargic than usual and drooling a bit. Me and my mom didn't think it was a problem so we didn't do anything. The next day his drooling had gotten worse and started to smell bad so I took him to the vet to get it checked out. The vet showed me mouth sores that had developed at the back of tigger's gums and said that he wasn't sure of the cause. He gave him antibiotics and told me to check back with him. After 2 days Tigger still was drooling and had stopped eating as much so I took him to a different vet for a second opinion. The second vet said to find out why the sores were there I'd have to get a bunch of tests done and hospitalize him because he was dehydrated. He quoted me at $2200+ and I couldn't afford that at all being an unemployed student(I had already paid $400 in vet visits). I took Tigger home and tried everything to get him to eat again, I even tried force feeding through a syringe. After the next two days of Tigger not eating I knew he would die of starvation if I didn't do anything. My only option was the Humane Society as recommended by my vet as a last resort. I gave Tigger away last week to the Humane Society and I've been crying non stop since then. They made me sign a contract that stated that they wouldn't tell me how he was doing and its been so horrible since. I don't know how he's doing, if they treated him or if they put him down. I wouldn't be able to live with myself if he was dead because I know it'll be my fault. What should I do? I really want him back but I'm scared the people at the humane society wont tell me anything.

At this point, there is really nothing you can do.  You signed him over to them, which gave them to right to treat him.  Sometimes turning a cat over to them is your last resort when there is a huge medical expense looming that you cannot afford.  Honestly, you don't want to know what has happened to him, just in case the answer isn't good.  I'm not saying it isn't good, but just in case. 

Sometimes not knowing is better.  What you DO know is that either way, he isn't suffering, which is good

Do not blame yourselve for what happened to Tigger. Given your circumstances, you did all you could; you did your best. As mrsgreenjeans said, he's not suffering. Thank you for helping him.