Probably not damaged is my answer but moisture and electronics do not play well together.
Over time, even a minute "drip, drip, drip" of moisture getting into the case could start causing corrosion. Like electronics in a humid area would experience. Still would take a long time as I understand your setup and environment.
That said, I do not understand touching the vent with sweaty hands to determine if the vent not wet?
Is there a specific reason for expecting the vent to be wet? Or just that moisture from your hands is collecting there and perhaps getting in?
If you must check, then use a piece of some super absorbent cloth to touch the vent. That will protect the vent from sweat and, if moisture happens to be present, absorb that moisture. Put the cloth right there and easy to pick up and to use.
All in all you have options: breaking the vent touching habit would be a good start and hopefully that will be easy to do.
And do see a doctor anyway. If the sweaty hands problem (and it is not an uncommon problem) can be resolved or reduced then there will be less moisture about and the entire issue likely becomes moot.