After I played football one day, there was this dead skin on my feet and it hasn't gone ever since. It pains when I squeeze it. Is it something inside?

Unlikely. If your foot was normal before playing football, and depending on your shoes/socks, you may have developed a callus in response to the pressure and friction. The callus is difficult to cure because you continue to walk on it, continuing the pressure problem. Try a pumice stone. Second, you may develop a plantar wart. That is problem for a dermatologist.
Probably Not. It would be very difficult to determine what it causing this without examining your feet. It would be unlikely that you would have something in your foot. It would be more likely that you have a fungal infection like athlete's foot (tinea pedis), or some other kind of rash. I'd recommend having this examined by your physician.