I had a similar experience the first time a dog had a broken toe and after that I left them alone-seems bandaging and splinting did more harm than good - just kept the dogs quiet (unghh easier said than done)
Def on the vet
you can get a nasty staph infection. We wound up with something oozy after a bandage and wound up (at the vets advice) a 10 minute daily betadine soak, oral antibiotics and I covered it with a sock inside and covered the sock with a plastic bag for short outside trips.
I swear by white toddler socks in my medical kit! Some with toes in some with toes out. Vetwrap is good for holding stuff in place but does not breathe very well and let air in.
This was Grim after an injury that went to staph. (toes swollen/inflamed) It was pink one day and this the next! Took a few weeks of daily soaks to clear up. And there was no broken toe involved. For this we were given a pretty strong antibiotic.