Squirrel or not, when the hand or finger is cut deep, we always want to make sure there's no damage to the tendons (the things that help move your hands and fingers).
You did the right thing by irrigating it out right away with warm, clean water & putting on some antibiotic ointment
. For deep cuts, try to see your doc within 6-8 hours - less chance of infection if you need stitches. Good luck!