Well, I don't think that exactly ever happened. There was a show from Season 25 that was shown on 123 Sesame Street where he was afraid to go down the slide because he might get hurt. That was episode #3199.
There was a series from Season 24 that was never shown on Noggin (although I think it should have). He broke his arm by playing Triangle Tag and ran over a bicycle. He went to the hospital, and got his cast put on. Then, the next day, he had to go back, and the Grand High Triangle Lover came to visit him in the hospital. In the next show, he thought of things he could do with his cast on. There were a couple of shows like this. And he also got upset that he couldn't play anything, because of his cast. Then, the day before he got his cast off, he was asking everyone to sign his cast before it comes off, but he does not ask his best friend, Oscar, to sign it. Oscar wants to make the cast even more messy, but Telly just thinks it's a trick, and Oscar wants to say "No." After that, he finally got his cast off. And there was one more show after that, where he still didn't wanna do anything even without the cast, because he might break his arm again, or break something else.
So I think you were getting those 2 confused.