Hi Carlos, this is an interesting question. Actually when you throw a football you need to use a lot of the muscles in your body. Going from the upper part of your body, you need to use your shoulder muscles, which support the arm and are active during the follow-through. The shoulder joints have several muscles that help the rotation of your arm, so you can throw the ball. The neck-shoulder muscle or trapezius is also involved.

You will also use the muscles of your arm (the triceps, the biceps, and the forearm), and the muscles of your fingers (in order to hold the football). All these muscles will work together and in different times in order to help you drive and throw the ball.

In the upper part of your body, there are muscles which will also be involved, they are the pectoralis major, the latisimus dorsi, and the subscapularis.

There are other muscles that will help you to stay balanced when you throw the ball, and you will need to use them; they are the abdominal muscles and the obliques. And you will also need the muscles of your lower body, which are called the calves, the quadriceps, the glutes, and the hamstrings.

I found on Internet a video showing the muscles used during the throwing of a football. You might want to watch it and I hope you will enjoy it:
video here