... Since you're saying the problem is worst today.
In short, we need to find out what causes condensation. Condensation is the result of warm, moist air 'condensing out' on a cool, dry surface. With that said, what is 'above' the ceiling (in question) that would make it cool? Perhaps the air conditioner needs to be RAISED up? Perhaps the duct is in DIRECT contact w/the ceiling, and it needs to be raised up (and COMPLETELY insulated; not just insulated on 3 sides)? Perhaps the AC Unit is OK and the duct is NOT sitting directly on the ceiling. Perhaps you have a high level of humidity in the room. To test out (cheaply) how high the humidity is, put a dehumidifier in the room that is having the problem. Keep you eye on the Drain Pan to see how much moisture is being removed from the air. AT THE SAME TIME, keep an eye on the ceiling to see if the moisture goes away.
You MAY need a more permanent dehumidifier installed. Perhaps you need to look to see if the duct(s) are in DIRECT contact w/the ceiling (and have that fixed too.) Remember: Warm, moist air that comes in contact w/a COOL/COLD SURFACE will cause condensation. You have warm, moist air in the house that's condensing out on a COOL/COLD SURFACE.
RE-read my post and make a note of what needs to be checked out. You said you don't have access to the attic. There SHOULD be some sort of 'access hole' to it (maybe in a closet or something.) If not, one may need to be created by a Pro, but I don't think ANYONE wants to work up there in this heat. I do wish you well.
My best to ya and hope this helps.
Jay J -Moderator
PS: Do you have soffit and ridge vents? Is the ROOF (I'm not referring to the ceiling) insulated w/soffit chutes? Is the roof insulated, period? If it is insulated, it better have chutes installed ALONG with soffit vents and a ridge vent. This is what keeps the roofline cool as well as the attic.
PPS: Want to know what I think? Based on what you've written, I think that ductwork is in DIRECT contact w/the ceiling, and that it needs to be RAISED UP and insulated on the 'bottom'.