Can one use terramycin ophthamlic ointment for swollen infected eye?

Usually yes. This is commonly used for eyelid infection. You may have to change antibiotics ff it does not clear up.
Swollen eyes. If the cause is bacterial and it is susceptible then it could be appropriate. Otherwise you can make a bad problem worse that can lead to scarring and blindness. Most" pink eye " is not bacterial. This should be seen and evaluated within a day if possible by an ophthalmologist if possible.Otherwise a physician should be seen an as emergency.