Thanks for putting up your question on Just Answer.
Technically yes your dentist is right but that is really the extreme end of the spectrum. Such extreme levels of infections are rarely seen nowadays due to the abundant availability of antibiotics.
Technically speaking, as swelling of the face should be taken very seriously. Infection from teeth, most commonly lower back teeth, can spread if not controlled. Our face is made of of muscles and bones, which have loose connective tissue between them. These infections are caused by organisms like Staphylococci and Streptococci, which have the capacity to release hyaluronidase, an enzyme that can break through these barriers.
Thus this infection can spread very rapidly.
If untreated for long periods of time, this can result in large swelling of the face, reduction in mouth opening and enlargement of tongue and neck lymph nodes, which can restrict your capacity to breathe which can be fatal. This is called as Ludwig's Angina.
But if you are currently taking any antibiotic then you dont have to worry about what your dentist said can happen. Apply as much ice as possible from outside.
Hope this answers your question.Please leave a positive rating for me if this answer has helped you. I do not get credit for it otherwise.