My nose is tender to the touch and turned red. No cut or anything but it is noticeably red and tender. Could this be cellulitis or an infection?

Could be several. different conditions, such as fungal or bacterial infection most commonly Erysipelas or Rosacea. Or it could be bad acne, or reaction to cold/heat. or a sunburn or chemical burn. Is it peeling? Is it hot and tender? Are there spots? Please see a healthcare provider for help with your condition.