Dose for Amoxi is 5-10 mg/lb bid. 125 mg bid is reasonable.
If the cyst is draining, hot/warm/wet packing would help keep the drainage hole open. If the hole is large enough gentle pressure would help get the thick sebaceous material out. If the cyst can drain on its own, surgical drainage can be avoided.
Once the infection is cleared and the area healed, removal of the cyst makes sense to avoid a repeat.
Let me know if you have follow up questions.