Thanks for putting up your question on Just Answer, and being very precise in providing the necessary information.
An infection (swelling, particulary) in the sublingual and submandibular areas should never be ignored or treatment should never be delayed.
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.
However, in your case, the offending tooth has been root canaled, and you already have been on antibiotics for 3 days. So the possibility of developing Ludwig's is very small.
1. Go see your Endodontist, an Xray will show how much of the infection has resolved after the root canal.
2. You may need a switch of antibiotics
3. Unless there is a massive swelling, external incision and drainage may not be required.
4. Extraction of the tooth is not required.
5. Keep applying ice from outside.
Hope this answers your question. Feel free to contact me again for more information. Please leave a positive rating for me if this answer has helped you. I do not get credit for it otherwise.
Good Luck !