Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
Call emergency services for bleeding that is heavy and does not stop with firm pressure, or for signs of a severe allergic reaction such as trouble breathing or swelling of the face or throat.
Contact your healthcare team promptly if you develop increasing redness, warmth, swelling, pain, pus, an unpleasant smell, fever, or red streaking from the wound.
Also call if the wound reopens, bleeding keeps returning, or you feel that part of the object remains.
Seek urgent assessment for new numbness, weakness, loss of movement, pale or blue skin beyond the wound, severe worsening pain, or an object near or in the eye.
Routine follow-up is appropriate if these do not gradually improve.
The article also says
Mild tenderness and a small amount of clear or blood-stained fluid can occur early in healing.
Every sign above is quoted from the sofidex article on Splinter removal. If you are not sure, err upward — it is always reasonable to be checked.