It certainly wouldn't have been my first choice of paint but if it's only a small spot and your pets don't get obsessed with chewing it you may be better off than using paint thinners to try to fix it, which now, having two days to cure, probably won't work anyway. Your only options are sanding or sandblasting. Just make sure the paint doesn't look like it will readily flake off. If it is flaky it will probably attract your chinchilla right to it and the chances of a concentrated exposure will increase.
If you do decide to strip it make sure to use soap, such as dish soap or degreaser, to remove any petroleum residue left behind by any thinners or cleaners, and then use a generous amount of water to rinse that off.
If anyone else has any suggestions your comments would be appreciated.