Go by the expiration date printed on the package. For most OTC medicines, opening the container doesn't start a shorter countdown — storage is what actually shortens a medicine's life.
Yes — Eye drops carries a printed expiration date and that's the date to go by. Eye drops are the one common OTC product where opening genuinely does start a clock: many multi-dose bottles carry a discard-after-opening instruction (28 days is a very common one) because the preservative only protects the bottle for so long once it's contaminated by air and the tip. Preservative-free single-use vials are meant to be discarded right after use — they have no preservative at all. Read your bottle and follow whichever date comes first. Not medical advice — ask a pharmacist or your eye doctor.
Room temperature unless the label says refrigerate, capped, and never let the dropper tip touch your eye or any surface. Heat and humidity shorten a medicine's real life faster than the printed date suggests, which is why a bathroom cabinet is the worst place for it.
Throw it out if you notice: Cloudiness, particles, or discoloration; A cracked or contaminated dropper tip; Any drop that stings unusually; Past the printed expiration date or the after-opening period on the label. Not medical advice — ask a pharmacist if you're unsure.