Hello and thank you for your question.
No this is not normal. This is a sign of an infection forming. What you have is a passageway from your mouth to your bone because the tooth is not in all the way. What you are having is bacteria getting under your gums and potentially infecting your bone. What you are possibly experiencing is pericoronitis
Its Symptoms are:-
-difficulty in mouth opening
(generally not feeling well)
(lymph node swelling under jaw)
Although not dangerous in itself, it can lead to greater infections such as ludwigs angina
which can be life threatening.
If you have a dental school near by or a Red Cross, they could potentially extract the tooth for little to no money for you. If you qualify for governmental assistance, you can get emergency dental work for free or for a few dollars.
This is something very important to get taken care of because if further complications arise it will be much more expensive down the road and potentially life threatening.
is only masking the problem and delaying the issue. If continued, the bacteria can become immune to the antibiotics and cause more complications.
Best of luck and I wish you good health.