My 2 year old daughter has a swollen toe, which is really red in colour. is it possible this is infected?

Yes-infection likely: The hallmarks of infection are REDNESS, SWELLING, pain, and increased warmth. Sounds like your daughter has at least 2 of these... I would touch it and see if it's hotter than the other toes and ask if it hurts. It's possible she has an ingrown toe nail? or sustained a localized injury that allowed an infection to occur. Best to show it to the doctor who can evaluate. It's very important.