Eyes itch after applying drops?

Recently got pink eye. Went to GP and got eye drops (chloramphenicol). I applyed drops to both eyes and they tend to itch. Is this normal? I didn't really apply it properly because some of it got on my lashes. As soon as I applied it, I just closed them, I mean like as soon as it touched my eye. It itches, so is this normal or have I done something wrong?