Teething?

My baby is 3 months (15 weeks exactly) .. Almost 2 weeks ago, my son was SUPER irritable (unlike him), drooling & chewing on his hand for 2 whole days which had me running to stores trying to find these that will soothe him.

After those 2 days, he was fine. didn’t need soothing at all.. still was chewing on his hand and drooling here or there but perfectly fine & showing normal behavior.

Fast fwd from 2 days ago to now— 😩

He’s still chewing his hand a lot, drooling a lot, not irritable like 2 weeks ago but is super fussy when he’s tired (very unlike him), starts to rub his eyes (which is normal) but I noticed he all of a sudden rub his nose a lot like it’s bothering him. but he’s not runny or congested. then, he’s hungry every 2 hours or less.. last but not least he’s waking up every 2 hrs at night 🙄 VERY ABNORMAL for him. helppppp..

Is rubbing the nose, frequent feedings & waking a lot throughout the night a part of teething? or could it be something else?