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There was probably no response because the expert is located in another country.
There are several reasons for a thumb to "pop" out of joint. It is also necessary to identify exactly which joint it is. If it is the one at the very base of the thumb where it connect to the wrist, possible causes are osteoarthritis, former or current injury, or repetitive motion injury. It is possible that you could have a torn ligament that resultsin the instability of the joint. Each time it pops out of joint it further injures the ligament.
Truthfully, the only way to know for sure is to have an orthopedist examine it and look at the xrays. As for what you can do until you see a medical provider, that would be to immobolize it. You can take ibuprofen for pain if you don't have digestive issues. Ice applied in a towel for 20 minutes 3 times a day will also help. If it isn't better in a week, you need to see a provider. Conservative treatment is what I have already described plus perhaps a steroid injection into the joint to relieve inflammation. If conservative treatment doesn't work over a reasonable time, then surgery to stabilize the joint would be the next step.
If you don't have insurance, there are many free clinics that can help you. There are lists below, but you may find other, more convenient ones, in your local telephone directory since not all local clinics make the national lists.
Please let me know if you have questions.