Yep. Plenty of drops burn a little.
Yes. Burning eyes after instillation of eyedrops is very normal. Most commercially prepared eyedrops contain preservatives such as benzalkonium chloride and stabilizers including glycerin and hydrochloric acid/sodium hydroxide to maintain ph. If you remember your high school chemistry, these agents are acidic/basic. If you ever squirted grapefruit juice into your eye at breakfast, you know that stinging sensation which results from the citric acid contained in citrus fruits. Same thing with the eye drops. Luckily, the stinging is temporary and the acids are not strong enough to cause any harm. If i had a penny for every patient in my office who told me the eyedrops burned their eyes, i would be a very wealthy man.