Lets see, the vet who went to school for 8 years gave you a medication, and billy-jo-bob and thelma said it was the wrong thing, and so you are asking perfect strangers? That makes no sense....
Now listen, its very sweet that you care approximately your buddy, most people wouldn't take a rat to the vet....so, at least give your rodent buddy the benefit of the doubt - and listen to the Physician, aye?
And yes, the lacrimal (tear) ducts will allow the antibiotic to treat the sinus...same way your tear ducts run out your face through your nostrils...
who prescribed the tetracycline whether it wasn't a vet? Get the object to a vet.