The question says "dig out." The sources that answer it use different verbs, and the difference matters.
The answer sits in two sentences
Cleveland Clinic says: "Ingrown toenails usually aren’t serious and you can typically treat them at home."
The same page then adds a limit: "If you have signs of infection or a severe ingrown toenail, don’t attempt to cut it yourself."
Where the wording stops
Look at the verbs. The first sentence says "treat," and the second says "cut." Neither one says "dig out," so neither one approves it. The second sentence also carries two conditions, signs of infection and a severe nail, and either one is enough to take cutting off the table.
The page does not list what counts as severe, so do not guess at it. MedlinePlus has an ingrown toenail entry and discharge instructions for ingrown toenail removal, which show what the office-side route involves.
What to confirm, and with whom
If the nail looks infected, or you cannot tell whether it is severe, ask a foot doctor in the Itasca area before you pick up any tool. Ask what they would call severe, and what they would want you to watch for afterward.
The clause readers skip
"Typically" is the hinge of the first sentence. It describes the usual case, and your nail may not be the usual case.