Does dental work such as fillings and extractions cause throat infections or cause you to spit up brown mucus?

It can. Extractions can cause a little bleeding and this can cause to spit up dried blood.
No. The treatment itself will not cause infections, but the underlying condition, as in a bad tooth that needs to be extracted might be causing an infection that requires an antibiotic in addition to the extraction.
A dental abcess. Occasionally a dental abcess may arise from a site of extraction if predisposing factors such as poor dentition/ dental hygiene, prior radiation therapy (ie. H&n cancer), severe smoking.

Related Questions

I had some dental work done and now I have some kind of infection in throat that makes me spit up brown mucus?

Dental work. Unfortunately, dental cleaning and any type of dental procedure can introduce bacteria into your bloodstream. This can be a major issue if you have mitral valve prolapse. In your case sounds like you have contracted a systemic infection caused by your dental work and you need to either contact your dentist, or general physician to determine if antibiotic intervention is warrented. Read more...
Coincidence. The throat infection is probably not related to the dental work but instead you are probably developing a cold. Read more...
Throat Infection. The dental work you had done and the throat infection most likely are not associated. If you have a throat infection see your physician or a ear nose and throat specialist. Allowing it to continue may lead to something worse. Read more...