Although breast cancer can affect women of all ages, it is extremely unlikely that your symptom is breast cancer
under 7% of all breast cancer cases occur in women under 40 years old
Is the burning feeling painful if you touch it? Are you on your period or is your period due soon?
I often experience breast tenderness in the week preceding my period. Though I wouldn't categorise that as a burning feeling, just soreness and a tight/stretched feeling.