It can. It's possible to allergic to any medication. If you think you are having an allergic reaction, see your eye doctor.
Yes, but. Virtually any drug can cause an allergic rxn in susceptible people. Latanoprost can cause redness, blurred vision, burning and the sensation that something is "in your eye" (foreign body sensation) which you may perceive as an allergic rxn but these are actually side effects.