I'm sorry that you feel like they spend time with you out of pity. It is possible, but it is very unlikely that it is the only reason they hang out with you.

I would not feel my friend (if i had any) pitied me if they said I had little or no friends, because it is true. I would feel bad about myself because it is true.. But I would not believe that their liking of me is now only pity friendship. Perhaps they feel a little bad for me, but anyone that cares would. It doesn't mean the friendship only continues because of that.

So, I don't think their friendship is pity friendship, but!

It is not Sam or Jay's place to speak of your private business like that to people. Social anxiety is a personal matter and people do not share others personal matters to guests that "stop by" or suggest it to their relatives, or even talk about it at all with anyone but you.

Personally, I do not tell people I have social anxiety. It is obvious enough as it is, and I feel I would not feel better if I told people. I instead tell people I am very shy, for it is a more socially acceptable way to describe myself. I am not suggesting you shouldn't tell people that it is social anxiety if telling them helps you, but if you're finding that it just causes you more trouble, saying you're shy might be better.

Or, when you tell people in the future, tell them it is a personal matter, and you are confiding in them because you trust them to keep it confidential. Make sure they understand you are seeking support, and that it is not a gossip piece. If you don't believe they are responsible enough to handle that, don't tell them.