i had the same problem in the bathroom of this house. draino didnt do shit to either.
the bathtub happened to have a lot of girls hair in the drain (girls lived here before), so i pulled it out (it was gross), but that solved the problem instantly.
as for the sink, i lived with it for a while, but it just got annoying, so i got a plunger and plunged ( :thinking: ) a ton. a lot of shit came out and it works fine now.