I have 2 cysts on my nose and 1on my chin, all of them under the surface of the skin, there tender, sore and redness around area. do i have infection?

Cystic acne: Cystic acne lesions commonly occur on the face in these areas. If you catch them early enough and don't squeeze them, I've found that applying OTC hydrocortisone cream can be helpful to reduce inflammation. Bacteria and hormone changes are factors. Oral or topical antibiotics, retinoids, oral contraceptives and/or Spironolactone can be effective. Steroid injections into the cysts can help also.