My lips are swollen, itchy, burning and they have a sort of rubbery feel when they're dry?

May be lip eczema: Persistent irritated lips can be lip eczema, which may be treated like skin eczema, using hydrocortisone cream (twice a day for 1 week) plus Vaseline or Aquaphor to retain moisture. Sometimes lip balm or lip sunscreen chemicals cause an allergic reaction. Other times, a person is a primary lip-licker (it's her habit). Once cracked, lips get irritated by routine foods and juices. A doctor can help.