Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
Acanthosis nigricans itself is almost never an emergency.
Emergency care is generally needed only for severe acute symptoms, such as difficulty breathing, fainting, confusion, or another immediate threat to health.
Seek prompt medical assessment if the skin changes begin suddenly, spread rapidly, involve the mouth, or occur with unexplained weight loss, persistent abdominal symptoms, loss of appetite, or unusual weakness.
Follow-up depends on the suspected cause and any test results.
If testing is normal but metabolic risk factors remain, a clinician may recommend periodic blood sugar, blood pressure, or cholesterol checks.
The timing should be individualized rather than based on the skin finding alone.
Arrange a routine appointment if new patches appear, existing areas become more noticeable, or you develop symptoms such as increased thirst, frequent urination, menstrual changes, or unexplained fatigue.
The article also says
If treatment is started, ask when improvement might be expected and how irritation should be managed.
Skin changes often improve slowly.
Photographs taken under similar lighting may make gradual changes easier to track.
Every sign above is quoted from the sofidex article on Acanthosis nigricans. If you are not sure, err upward — it is always reasonable to be checked.