Im a General Contractor and an Electrician, Built Commercial plants for about 10 years.
My guess would be that the compressor is the tipping point on the breaker. A 15 amp can normally hold alot. If the circuit is already loaded it would not take much for the Compressor to trip it.
Could be a number of things. Without see'ing it i couldn't tell you for sure. But 1. could be a bad breaker ( Some will go bad). 2. Could also be a bad ground. Or 3. could just be overloaded.
If you want a 20 amp circuit, you need to make sure the existing wire is 12/2 ( 2 wires, b&w and a bare ground) . Depending on the age of the home you can identify it. Older homes most often have 12/2 in my experience. can be cloth or white. Early to late 80's they started using 14 ga which is now white for 14/2 and 14/3 and they started making the casing yellow for 12/2 and 12/3. If it isnt 12 ga you will need to run a new circuit.Depending on what you want and where you want it; it can be run in a number of ways. Normally can fish them in the wall with a little work and the right tools.
Hope it helps, If you have any specific question feel free to call me, five3zero 3nine1-7 four45
James