It sure could be a poor connection at that outlet, and it could be dangerous: if the connection is arcing it could generate heat without tripping the breaker. Kill the power to the circuit by tripping the breaker, and have that outlet inspected.
If the wires have been backstabbed instead of screwed down, consider having all the outlets in the house reworked to use the screw terminals.
Also consider having the breaker that's been tripping replaced with an arc-fault (AFCI) breaker. It won't trip any less, in fact it may trip more, but it'll protect you from arcs in these bedroom outlets. AFCI's are now mandatory for new work on all bedroom circuits in most places in the US and Canada, to protect against exactly this risk.
The problem with the tripping won't go away until you have a dedicated circuit put in for the A/C and/or the hairdryer. 15A among several bedrooms including A/C and a hairdryer isn't nearly enough.
Chip C Toronto