I would recommend that you see your doctor
back next week as it sounds like you have already scheduled. The definition of an abscess
is an infection below the skin that leads to a collection of pus. You are right that most abscess do require draining in order to heal properly. However, if the area that you are feeling is hard, rather than soft and boggy in texture, the likelihood that there is any pus inside of it that can be drained is very very low. It sounds like you have already seen three doctors
about this issue in a short period of time, and they have all had exactly the same opinion - namely, that this is not an abscess and that it cannot be drained at this time. I would be inclined to agree with them and to make the recommendation that you follow their advice in terms of treatment and followup. Clindamycin is an excellent antibiotic that is often used for superficial skin infections so if your doctors felt there was evidence of an overlying skin infection then this would be one of the first line antibiotics for treating this condition.
Again, I would recommend that you see your doctor back next week as it sounds like you have already scheduled. In the meantime, if things get worse you can always call them again to let them know what is going on and get more advice.