Hello eselgee and welcome to The Community!
Yours is a common question whenever a circuit becomes overloaded, tripping the breaker.
The purpose of a circuit breaker is to protect house wiring from overheating when too much current is flowing. The size of a breaker, rated in amps, is chosen to match the size of the wire in that circuit so that it trips before the wiring can catch fire. In most cases a 15 amp circuit breaker is used with 14 gauge wire, and a 20 amp breaker must have at least 12 gauge wiring. Please note that as the wire gauge number goes down, the wire size gets thicker and can handle more power. For this reason, I do not recommend that you simply replace a 15 amp breaker with a 20 amp one.
Over the course of many years, breakers can wear out and trip sooner that they should. You may want to consider replacing the old 15 amp breaker with a new 15 amp one.
If you need to increase the power handling capability of this circuit then I recommend that you have a professional electrician upgrade it for you. He or she will ensure that all the wires, switches and outlets will match and meet code requirements.
I hope this helps,