Tip of nose dry and rough textured. put moisturiser and it burns. slightly red and blotchy. never had this before. what should i do?

Solar damage: If you are 23 then it is probably solar damage to the skin. It would need to be seen to rule out a early skin cancer. If hydrocortisone cream 1 % twice a day helps and it disappears then it is unlikely a skin cancer.

Unsure: Know what your know and what you don't know. I would have to see it and examine you to render an opinion. You need to see a physician and be prepared for an uncertain response. I would speculate that it may be an eczema and a steroid cream would be tried, but a wart, or seborrhea are possible. You will need to see someone for this