A trip to a Herp vet is a good idea. In the meantime, you can apply a plain (no painkiller version) antibiotic like Neosporin, Bactrin, or Silver based gel daily with a Q-Tip. Also, would look over it's enclosure to insure there are no sharp items in there or areas where frog could hurt itself.
Please read this excellent care article: Frog Forum - White's Tree Frog Care - Litoria caerulea. As you can read in it; need to provide frog with a basking area that reaches 85F during day. Enclosure temp can drop to 75F at night. When full grown your frog will require a larger enclosure, around 18x18x24 in. is minimum I would recommend. Good luck!