I had this exact problem with my White's very shortly after getting him. I actually got him in my aquatic science class for our group aquarium/terrarium project when another group wanted one and were told they had to purchase more than one. So basically my group ended up with a frog we knew nothing about and gave him a very small space above our aquarium.
The tank was way too humid, had horrible ventilation and he would regularly jump into the water part of the tank, swim to the other side to attempt to escape then swim back to his side. I now know we were doing EVERYTHING wrong. After some research, when I got back to school (our tanks were kept there because the teacher provided them) I noticed whitish spots on his back. I spoke with my teacher and she gave me a 10 gal tank to move him into since I now knew he needed a much bigger area and shouldn't have access to deep water, among a bunch of other things. I'm lucky he didn't drown. But anyway, I researched the spots because I didn't want him to die and nobody else in my group cared enough to look into it. The vet was out of the question because it was too expensive and nobody in my group was willing to chip in.

SO after lots of googling I was pretty sure it was a fungal infection and found out there was a home remedy that might work and thought I'd give it a shot, though I was doubtful.
The website I read told me to bathe him in a 2% solution of mercurochrome (or malachite green) in water. Obviously the mixture needs to be shallow so that the frogs head is above the water. So I got malachite green and brought it back to school. I used a small bowl for the mixture then put my White's tree frog in it. By this point he was so sick that I didn't have to worry much about him trying to escape. Plus they love sitting in water. I left him in it for 5 mins (that's the recommended time, I wouldnt risk keeping him there any longer). You can do this every day, but only once a day until it gets better. If it doesn't improve after a couple of weeks though, a vet is your next option. It worked for me after 3 or 4 days, and I took frogger home after this ordeal and he's been mine ever since. Nobody else in my group wanted him and I fell in love with the guy lol.

I know this response is a little late but when mine was sick I had a hell of a time figuring out what it was so maybe this will help somebody