Getting hit in the nose has a different feeling from getting hit anywhere else because the nose is a particularly sensitive part of the body. The nose is full of nerve endings, meaning that it is very sensitive to touch and pressure. Additionally, the nose has a direct connection to the brain, so any sensation of pain or pressure that is felt in the nose can be felt more prominently.

Furthermore, the nose is home to a number of delicate and important internal structures, such as the sinuses and nasal cavity, which can be damaged easily by a hard blow.

It's one of the few immediately hittable features with a lasting sensory effect. I've never been punched in the tongue, but i imagine it would feel different from most other places.

I think it has to do with the fact that when you're hit in the nose, you experience all the other normal "getting hit" effects, but in combination with them, there's also the way it affects your smell perception and the way your brain processes non-smell signals as smells. There are a lot of nerve endings in that area the typical of which is interpreted as smells or nuances of smells, and after a hit they're firing due to swelling, damage, etc.

I'd hazard a hypothesis and say it's because of the noses extra pressure sensitivity, when your nose is hit (the outward center of your sinuses, which connects either directly or indirectly every sensory organ in your head) the rapid pressure change is sensed along with the standard impact and pain. whats happening is two senses are being activated at once, versus being punched in the side of your face really only activates one type of sense, being "standard" pain, think of it like when you're eating and you can smell the food so the food is far more delicious. When you cannot smell the food you are eating, the flavor is much more mild and the experience is less rich because only one sense is being activated. when both are activated your brain combines the sensory information into one experience and makes it far more enjoyable, same with the nose being hit, two senses versus one being activated, so the experience is far stranger and almost has a third "dimension" to the pain.