Can i give my 2 month old baby tobrex eye drops, she has a pink eye which she possibly got from my 2 year old?

Ask baby's doctor: A baby with "pink eye" usually has a viral or a bacterial infection, or sometimes other problems (which are unlikely at 2 months). In a 2 month-old, doctor can examine now to get a diagnosis. In older babies, symptoms may go away in a few days or up to a week or so. Pediatrician often will check a child if symptoms haven't gone away in a week, or if there are other symptoms such as fever or pain.

Evaluation : Most probably your baby has the same infection as her sister. The other consideration at this age is birth related infections. If there is a cough and cold symptoms in particular, please see your pediatrician.