Yes, it is possible to feel nausea because of drinking eye drops. I don't know you drink it, which seems so weird. But when instill eye drops, it is possible and common to get the eye drops drain from eyes into nasal and finally into throat. As we know, most part of eye drops is saline water. To achieve different purpose, it will contain different medication, for example, steroid, antihistamines, erythromycine and so on. Usually moisturizing eye drops contains no other medication but just saline solution. However, no matter what kind of medication it contains or not, most eye drops are used to reduce the infections or inflammations or increase the lubrications, it is far less harmful than any other oral medicine. Usually these eye drops might cause a stinging in eyes, but it won't last for long. Other side effects from different medication might include soar throat, allergy, itching, swelling, fever, rash or even difficulty breathing. If you threw up the eye drops you just drank, it should be OK. But if any symptoms persist or get worse, you need to see your doctor at once. In a word, before you take any medicine, you should let your doctor know your medical history in case any serious problem caused. If you want to avoid eye drops travelling down to throat, you can't do a little tender massage at the cornner of your eyes, next to your nose bridge, for a few minutes. It could effectively help prevent the eye drops draining down.