Im just trying to make my skinny arms bigger. Can just doing pushups and lifting a 25 pound dumbbell make me bigger?

I currently do 12 reps on one arm without stopping and then doing the same on the other arm using just one dumbbell. Is that fine or is it better to have two dumbbells and alternate sides after each rep?

I am a guy and aged 16. I have just bought a pair of dumbbell and wish to tone up my arms and upper body. My arms and chest are saggy, so i wish to use a dumbbell to tone them up. How many times should i do in a week to see improvement and what are the ways to use the dumbbell correctly. My aim is to tone up my arms and chest in a month, can that be possible?