No no no no no, the additional load capacity is also dependent on thicker wire. If you change the breaker on 14ga you will cause an electrical fire,
the fire investigator will discover the thin wire,
you will get fucked on the insurance payout/lack thereof,
you will get fined by L&I,
you may be prosecuted,
you will get sued.
Moreover you shouldn't have used a 20 amp receptacle unless you were positive the circuit could support the load. 20 amp receptacles are specifically identifiable as such for a very good reason, and should not be abused just because they're easier to install. Even if you leave the 15 amp breaker in there, you're opening up the possibility of a future owner unknowingly swapping it out for a 20-amp breaker and burning the house down. Take out the 20-amp outlets unless you can confirm the circuit can support the load.
Right off the bat you need to buy new 15-amp outlets (they're useful to have lying around anyway). Clamp-style is significantly more prone to premature failure. Open the breaker, take it back apart, and identify the gauge of the wire. If it's less than 12 gauge copper it cannot safely handle more than the 15 amps. If it's Aluminum, you're fucked and really shouldn't have an outlet on that circuit at all.
Is the breaker off? Yes? Good.
Once you have the junction box exposed, you're almost ready to start.
You'd better check the breaker again.
Note: Black goes to the dark screw, white goes to the light screw.
Also, check the breaker again.
Bend each of the three wires in a loop, preferably a little more than 180° and about 1/4 inch wide.
Make sure the wire stem is on the left and loops to the right, so when you tighten the screw it will also tighten the wire. Do this for the ground (green/bare copper), negative (black), and neutral (white).
Wrap electrical tape around the sides of the outlet in a loop 3-4 times, and put it together.
tl;dr For a 20 amp load on the outlet
the wire must be 12ga or thicker,
wire must be copper,
the breaker must be 20 amps (less will trip low, more will cause a fire),
the receptacle must be rated for 20 amps,
the receptacle must have a functioning ground.
Any less will kill you and your family eventually.
Now stop asking for electrical advice on reddit and call an electrician.