Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
Emergency care is needed for trouble breathing, faintness, throat tightness, or swelling of the face, lips, tongue, or eyes after using an acne product.
These may be signs of a serious allergic reaction, which is rare.
And for anyone, someone who:
Stop using a new skin product and seek prompt medical advice if it causes severe burning, blistering, marked swelling, or a widespread rash.
And for anyone, someone who:
Routine medical follow-up is appropriate if blackheads remain bothersome after a consistent trial of appropriate over-the-counter care.
An appointment is also reasonable if the skin becomes repeatedly irritated, if acne is leaving marks or scars, or if it is affecting emotional well-being.
The article also says
Seek earlier clinical advice if blackheads occur with numerous painful nodules, rapidly worsening acne, or signs of infection such as increasing warmth, swelling, drainage, or fever.
These features are not typical of uncomplicated blackheads.
A solitary dark spot that changes, bleeds, does not heal, or looks unlike the person's other spots should be examined rather than repeatedly treated as a blackhead.
Every sign above is quoted from the sofidex article on Blackheads. If you are not sure, err upward — it is always reasonable to be checked.