Will doxycyllin be effective in the treatment of a sebaceous cyst?

Not exactly...: Antibiotics (such as doxycycline) can help to treat / prevent worsening infection of an affected sebaceous cyst. However, it does not get to the root of the problem, which is that there is a cyst underneath your skin. To fix the problem permanently, your surgeon will need to completely excise the cyst (preferably at a time when it is not infected).

Doxycycline is: an antibiotic, and will be effective in infections caused by organisms which are sensitive to it. If your cyst is infected with staph, it could sometimes be effective in treating the cellulitis portion of it. If it is already abscessed, your cyst will need surgical drainage.

Maybe.: It should cover MSSA and MRSA but you may need to have it incised and drained if not done already. Was it cultured? Not absolutely necessary but that would tell you for sure. Usually, incision and drainage with possible packing of the wound is all that's needed. Abx may be useful with ruptured sebaceous cysts and widespread infection.

Infected?: Abx will NOT cure a sebaceous cyst. They can help clear the infection and surrounding cellulitis that can occur when the cyst becomes infected. .... but not the cyst itself. The cyst needs to be removed if bothering you. If not bothering you can be safely watched.