You had your tanning sessions prior to application of the acne cream or have you started applying the acne cream even before the tanning sessions?
This may be an allergic reaction to the tanning sessions which could have been aggravated by the previous applications of acne cream/ solution.
I suggest that you seek a prompt consult with a dermatologist. If this is contact dermatitis or allergic dermatitis you need topical administration of corticosteroids or if indicated oral medications.
Do not scratch or pick on the affected skin. Avoid any tanning sessions and stop using the acne cream until this has been assessed by your physician.