Your landlord might object to you hiring outside help to look at their equipment. Or might not. Either way I would contact the landlord and express your intentions.
Providing landlord gives green light, next challenge is to find a certified, competent pro who wants to work on rental property. Contractors can be reluctant to do this because prior experience with landlords objecting or tenants not paying leaves a bad aftertaste.
Psychrometrics: the very foundation of HVAC. A comfort troubleshooter's best friend.