Looking at the shape of the injury, the sores/cuts are triangular in shape.. is what he was pushing on triangular? I am no expert in treating tree frogs, but using Neosporin w/o pain reliever sounds like the way to go. You will want to address the enclosure though, if your Whites is injuring himself in an attempt to escape, there is definitely a problem. Your frog really does need foliage and branches to climb on. Also what is the temperature/humidity in the enclosure?

If you want to get the actual volume of the enclosure, measure the Length X Width X Height / 231 that will tell you how many US Gallons it holds.