If you ran 12 gauge wire, then you can use a 20 amp breaker. Otherwise,
leave it at 15.
What is the size of the A/C? If you are talking about 5,000-7,000 BTU.
It should be OK.(5-7 amps). You might see the TV flicker a little. I
had this setup for years in my bedroom and it never gave me a problem.
If you are talking about a big unit, you are better off running a new
line. Run a 12/2 w/ground so you have the option to get a 220V unit.