My one and half month old has allergic conjuctivitis, can I use tobrex (tobramycin) to treat?

No. Do not use any medications for your baby that are not prescribed for your baby for that specific thing. For now use a cool washcloth to remove any drainage and take your baby in to her doctor for evaluation. It is unlikely that what she has is allergic at her age.
Nooooo! that is not used for allergies, and it may not even be allergies, may just be immature tear duct. See the pediatrician.

Related Questions