What does tobradex (tobramycin and dexamethasone) antibiotic do?

2 things: Tobradex (tobramycin and dexamethasone) is an antibiotic / steroid combination and is good for conditions where you have both a bacterial infection and inflammation. Or it can be used to treat inflammation and prevent an infection. The steroid part does have potential side effects (glaucoma, cataracts, etc) so use with caution.

Combination treatmen: Tobradex (tobramycin and dexamethasone) is a combination of tobramycin and Dexamethasone available as a drop or an ointment to treat superficial infections of the eye surface. It is effective and is especially useful in ordinary staphylococcal infections. Your ophthalmologist can determine the best use of these medications.