I've been sneezing up a storm lately, but no itchy eyes, hoarse throat etc. that'd suggest it's allergies.

Still likely: Allergies don't have to affect anything other than your nose, so it still could be allergies. Anything that irritates the lining of your nose, like pollen, pepper or even some new lipstick or makeup that you put on your upper lip could be doing this. I'm sure it's a nuisance but it's not dangerous. Noses like to clear themselves out especially if irritated, and that's often a good thing!

Could still be: Allergies. Allergic rhinitis can presents with postnasal drip, cough, itchy ears, itchy throat, irritability, and fatigue but more commonly just bouts of sneezing, rhinorrhea, nasal obstruction, and nasal itching. You can have allergic conjunctivitis(itchy watery eyes) at the same time but don't have to either. You could consider a trial of antihistamines to see how your body responds.