Great question!
Depending on how long the piercings have been present, they might close on their own, however if they have been there for some time it is possible they won't unless you have something done. Essentially the way to address these holes is to remove the tract, which is the area that...
At day 33 your neck still looks much better than the preop.
Ask your doc if you can have lymphatic facial massage. Be patient. It looks like all will be well.
Stick to fillers. Anything surgical can potentially have a problem requiring additional surgeries which could get you into a financial mess that you are obviuosly trying to avoid.