Hi! Yeah, putting a frog in with geckos might not be the best thing. Different temp and humidity requirement for one thing, also the danger of the frog eating them, which I'm sure you've read about!

His nose should heal fine on its own. If it becomes infected you could try putting on a bit of antibiotic ointment, but you'd need to make certain it didn't have any painkillers because those are lethal to frogs.

One thing you can do is to check the top corners of any tank for sharp edges and find a way to file them down or something. Mesh screens on top of tanks can have loose threads at the edges so be sure to check those.

Sometimes frogs just get nervous being in new places or are just restless. The best things you can do are to keep the tank covered or out of high traffic areas for a while. It's also good to make sure the temp and humidity are comfortable.

I'm glad you're happy with your new frog, though. White's are adorable and though they mostly sit, watching their acrobatics can be very entertaining.