Logically speaking, when the body is weak in general (could be from delivery, from sickness or even low immunity), sitting in a room that's too cold can be quite uncomfortable. Even if you are not in confinement, prolonged exposure to the cold without proper cover and clothings will make you sick eventually.
However, in a humid climate like the region's, it's a bit impossible to go without air con and fans. Wearing long sleeve clothes can be quite uncomfortable as well. I'd say everything in moderation and as for the long sleeves, if your elders do insist on it, maybe you can get those that are made of woven material, the kinds that are light and airy instead of thick sweaters and cardigans.