One eye burns. Should i be worried?

You should have checked your eyes with any Ophthalmologist.  As you are saying it as pink eye that means you are having some conjuntival ( hope fully ) or ciliary congestion ( when the pathology is in cornea). You didn't told which drop you are using . Was it prescribed by any Ophthalmologist? One thing I want to clear here that you will feel burning sensation when you use any drop during inflammatory conditions of eye ( when eye becomes red). It's quite normal, nothing to worry about it. Just go for a eye checkup whether you are having conjunctivitis  ( viral / bacterial / allergic) or having other eye problem?         In this season we are seeing lots of cases with viral conjunctivitis.  So don't worry . Go for a checkup.