Can I replace a 15 ampere circuit breaker with a 20 ampere breaker?
No!

The only safe way to increase the circuit's capacity is by replacing the wire with one of adequate gauge.  For 20 amps, 12 AWG copper is adequate for up to about 100 feet.

If you simply replace the breaker, the wire can overheat and ignite the building from inside the walls.

To resolve the dimming issue, check that the outlet is in good condition and that the wires are securely fastened and not showing any signs of overheating:  blackening or loss of the copper shininess.  Also, check the end of the wire inside the service panel, both neutral and "hot" (black) wire.  If those are okay, set the appliances to a lower wattage setting or replace them with lower wattage models.