Inground Pool Setup Needs More Power
You could try the following to determine the gauge


Cut the power off
Open the connection and pull a wire off
Use a wire stripper and find the largest hole it fits in


As to the rest of the question...

25 amps is nuts. You have 18 amps so a 20 amp breaker on 12 gauge wire should be sufficient. My bet is that, since you have a 15 amp breaker, that your wire is 14 gauge (it's pretty rare to find higher gauge wire on a lower amp circuit like that). When in doubt, run new wire. It's not worth it to try and guess. Know that your setup is sufficient.

I would suggest dropping new 10 gauge wire (more than you need in case you ever add anything else, like a Polaris, although you'll probably want a subpanel at that point) and adding a 20 amp breaker. If you're burying it, make sure it's UF and preferably in conduit. Take the existing wire and stick it in a box with a GFCI and make it an outlet.