What are eye pain in one eye (throbbing) and a splitting headache in the same side of your head symptoms of?

Various. Acute angle closure glaucoma, subarachnoid hemorrhage, ruptured aneurysm, giant cell arteritis, orbital infection, herpes zoster or trigeminal neuralgia, cluster headache, trauma, etc.
Cluster headache? Acute onset of orbital pain and headache may be a sign of cluster headache. Usually the eye tears with this. If you have throbbing, this may originate from an aneurysm. Best to get checked out for this soon. Other causes may be trigeminal neuralgia, atypical migraine, etc. An ophthalmologist can help sort this out - call soon.