Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
Seek emergency care if you become confused, faint, very unwell, or have other signs of a severe, rapidly spreading infection.
Arrange prompt medical advice if the toe is increasingly painful, produces pus, or develops redness and swelling that are spreading beyond the nail.
You should also seek care if home measures have not helped or the nail keeps becoming ingrown.
Do not wait for the pain to become severe, because reduced sensation can hide worsening injury.
Get urgent same-day help if redness is spreading quickly, the toe or foot becomes markedly swollen, or you develop fever or chills.
The article also says
Do not try to cut out the nail yourself if it is deeply embedded or surrounded by swollen, bleeding tissue.
Seek early professional care for any foot wound or suspected infection if you have diabetes, poor circulation, reduced sensation in your feet, or a weakened immune system.
An ingrown toenail is rarely an emergency.
Every sign above is quoted from the sofidex article on Ingrown toenail. If you are not sure, err upward — it is always reasonable to be checked.