I am in a bowl of soup, apparently. 😒 (East coast USA)
Your apartment AC running short cycles is probably the root cause of the high indoor humidity. It's possible there's also a condensate leak somewhere, which is always fun. Either way, if the landlord won't address it, I can only assume what they really want is a building full of mold, not people. 🫠
A standalone AC that you control is probably going to work better than a dedicated dehumidifier, just due to the ducting that AC takes into account but dehumidifiers typically don't. For direct, immediate help for your ickiness at least, get some air moving. Cheap box fan is fine. It won't change the humidity but it will help evaporate your sweat.