House is not canonically autistic as far as I know. Of course, in TV writing, autism tends to be sloppily coded as "being an asshole" instead, and he definitely is that in spades. He does seem to slightly play into it in one random episode, and his boss says something along the lines of "you don't even have Asperger's!" The only unambiguous autist on House that I remember is the kid from that same episode, who is nonverbal and melts down over the slightest thing. As far as representation goes, that's fairly narrow and not all that positive.

I watched The Good Doctor for about two and a half seasons. Eventually it started grinding my gears because it keeps being the exact same conflict over and over. (Ironic given I watched House, I know. Multiple times. Still.)
While whatshisface might be understandably "stuck", all those highly trained medical professionals and romantic interests around him should probably eventually have gotten a clue about that whole autism thing. As representation goes this guy is also relatively out there, and plays up a lot of stereotypes that don't seem entirely positive.
I do think the pandering/romanticization is kinda obvious in this, though: it plays up Super-Autist ideas, and makes sure there's no shortage of pretty girls around - who tend seem rather more into autistic guys than I daresay seems likely in real life, for some reason.

BBT I found mildly clever for like 5 whole seconds at the very start of episode 1. I don't know why I watched a few seasons further.
I dislike Sheldon's character. He is the archetype of the lazily written Hollywood "autist/smart guy/douchebag" pigeonhole, heavily playing into truckloads of strictly negative stereotypes about autists, smart people, geeks etc. and any combination. You know he's smart because he has the whiteboard with Physics on it, and because he's an asshole - one of very few ways TV writing tries to show intelligence at all.
Now I might seem butthurt - that would be because I started out with actual expectations of a "smart, geek-friendly" comedy show. Eventually I got more a bait&switch "cringe comedy" feeling (a genre I hate) with a superficially "geeky" paintjob.
Seems a bit pandery to me, mostly along the lines of antiintellectualism and "anti geek sentiment".