Hello and thanks for researching this very important question!
Overgrown teeth can be snipped at home with a pair of sharp wire nippers. You must have a steady hand and good eyesight!
You may need assistance if she is very wiggly or your hand is unsteady.
These teeth have a blood vessel in the center that allow the teeth to continually grow...be careful to snip this tooth back a bit at a time. Cut just enough today to provide relief. Wait a few days, then begin shaping the tooth back to its normal size.
You will probably have to watch and trim this tooth regularly, along with its mate.
Since her face is being injured, she may need medical attention if she is not eating or drinking, or seems tired and sickly. The cost of the visit plus the antibiotic will vary depending on where you live and whether the vets in your area consider hamsters an Exotic species!
Do ask the receptionist for an estimate of costs if you need to have her examined.
An otherwise healthy hammie can heal quite nicely at home as long as the cause of the abrasion is removed.
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