I don’t know any fool-proof way to know if you have such a problem.
Some people who have had low chronic infections i.e. feeling sick while there has not been anything wrong recognized by the traditional medicine (i.e. infection not even showing up in the blood samples) have found relief after removing all teeth with root canals. My dentist has also done some published research on this subject, but it is not knowledge mainstream dentists are familiar with.
However, it is probably not enough to remove the tooth, it must be cleaned properly as well, so you better talk to a natural dentist. Regular dentists think infections heal themselves, and sometimes they do, but apparently not always.
In any case, you should not take medical advice from random internet person and I am not qualified to give any, so the above is not medical advice.
I have not read it myself, but the book Accidental blow up in medicine has been recommended to me on this subject.