you have sinusitis, the dry air irritates the sinus and causes inflammation hence blocking air flow through your nose.

1. turn off air con when the air is cool enough for you to sleep.
2. add humidifier because the dry air is the cause of this problem.
3. set a higher temperature for the aircon and test whether it works so that the air wont' be too dry and irritates your sinus. every individual is different.

its quite a common problem. but only some people's condition will only get worse.
I had an Endoscopic surgery due to this issue cuz it went from bad to worse but that's the last resort.

he mentioned that his nose were blocked, tonsils wont block off the nostril airway. I know of the case you mentioned and i had tonsillectomy done on my tonsils as well

yeah, you can visit the ent and they will prescribe you antibiotics to reduce the swelling as well as nasal spray etc to clean your sinus and also will tell you the same thing to avoid it from recurring again.
for me, i still sleep in air conditioned room, been in dusty environments which only aggravated my nose and after a few years, new problems appeared due to my sinus. and i decided to have it removed and never been happier.
it was affecting my sleep so badly to a point i had to cut it off.

non inverter i set 25c