After I use tobramycin and dexamethasone ophthalmic eye drops, can I put my contacts back in?

Depends. If you have been placed on these eye medications, it is possible that there is a surface problem on your eye for which wearing contact lenses might be harmful or dangerous. Clear this with your treating ophthalmologist (you are seeing a real doctor - an eye md or ophthalmologist/ rather than an optometrist for these type of drugs)?