Thank you for choosing DoctorSpring.
The treatment plan by both the Doctors are acceptable. They are two different approaches, and both are acceptable. Since you second Doctor left it rather open he/she expected self drainage of the cyst followed by healing.
As of now you have some discharge and when you press there is more. In that scenario a minimal exploration is warranted. You can go to your current (second ) Doctor. He will look whether there is any pus to be drained.
Pus if any has to be drained regardless of the approach. In the first scenario your Doctor was draining it and keep the wound closed. Your second Doctor was letting it for open drainage. Now since there is some pus drainage when pressure is applied you need to make sure there is no organised pus.
Continue the antibiotics. If the pus drainage persists you should consider a pus culture and sensitivity test for antibiotics. I understand that this can be really frustrating, but thankfully most of these kind of lesions will heal in few weeks.
PS : If you have not tested you Diabetic status, you need to do a screening by doing a fasting blood sugar.
Hope this clarifies.
Feel free to ask followups/ clarifications