Does dry socket heal on its own?

Yes, but very slowly: You are much better off returning to the dentist who did the extraction to have it treated. Dry socket is very painful precisely because it is not healing.

Check meds: Since you are 34 Y.O., it is less likely, but anyone on osteoporosis medication should check with a dentist (especially if the dentist was not informed of your medications). It is more difficult that dry socket heals on its own if you are on this medications--route of administration, and dose, and drug type all affect the outcome. For future oral surgery, always be thorough reporting your meds.

Better option: Is to see your dentist as soon as possible for several reasons. First- you want to ensure that there is no infection present. Second-dentist can apply medication so that pain relief is simple and quick and will promote faster healing. Third- why suffer unnecessarily when this type of post operative treatment is generally at no cost to you as part of follow up care? Finally (see comment) -->.