How can I use another phone's camera in place of my camera?
Here's my suggestions:

Firstly: If your phone has a front-facing camera, use that.
Secondly: grab a can of air duster and spray the rear-facing camera out( if this clears it up, then find a crystal clear tape and cover it. Or get a case that covers it.)
Lastly: I'm taking the assumption that you do have another phone. If so, just take the photo and transfer(via bluetooth, text, cloud, etc.) it.

Hope something helps.
T.Swain