the thing you need to worry about is tetnus if the bit broke the skin
they can carry rabies but its unlikely
from web page
It is unlikely that a squirrel will bite a human hard or deep enough to require stiches, but infections are always a risk. Those bitten should wash the wound site and surrounding area with soap and water. It is acceptable but not necessary to further clean the wound with an antiseptic agent such as isopropyl alcohol or diluted hydrogen peroxide. Deep wounds should always be examined and cared for by an appropriate medical personnel.
Tetnus shots are important for such bites. The recommendation is to get a tetnus injection or a booster shot within twenty-four hours of the biting incident if the person bitten has not had such a booster within the previous five years. Rabies may be carried by squirrels, but this is rare.