You are somewhat at the mercy of NVC. "Sent to NVC" only means they strapped it to a turtle's back and hope the turtle will eventually wander to NVC. Seriously, though, it takes 2-4 weeks for NVC to receive your petition and another 2-3 weeks for them to assign the MNL case number. Both of those are estimates. It can take longer, or it can be quicker. Start requesting the status from NVC in a couple of weeks using the public inquiry form online.
Once you get the MNL case number, things are somewhat in your control. With the case number, you can complete the DS-160, pay for it, and then schedule your interview. I read that SLEC is backed up right now. Hopefully that will clear up before time for your medical exam.
A fairly reasonable estimate to POE would be 3 months if you push once you get your case number. 1.5 months until Manila receives your petition, then another 1.5 months for interview, medical, and CFO. There are always variables, so be patient. For example, my petition took 2.5 months just to GET to NVC, while some others with the same NOA2 took only 2 weeks. I think it was that turtle's first trip. You're almost there...