Start with a limit, because it shapes everything below. There’s no warning-sign list just for the shin. Pressure sores form over bony sites such as the buttocks, elbows, hips, heels, ankles, shoulders, back and back of the head. Venous ulcers usually form on the leg above the ankle. Ulcers from poor blood flow show up on legs, ankles, toes and between toes.
What applies instead is the general list. Contact your provider right away for redness, increased pain, or yellow or green pus, or excessive clear fluid around the injury. These are signs of infection. Also contact your provider right away for black edges around the injury. This is a sign of dead tissue.
The more useful question on a shin is what kind of wound it is, because the specific signs differ in ways that change how you read them. With a venous leg, the skin around the wound may be shiny, tight, warm, or hot, and discolored before any infection — so warmth tells you less there. A leg with poor arterial flow may be pale and cool, and turn red when hung down. A wound from a knock or a scrape on an otherwise healthy leg has neither baseline, so ordinary redness and warmth mean more.
So the thing to work out is which leg you have. Early signs of venous insufficiency include leg swelling, heaviness, and cramping, and dark red, purple, brown, hardened skin (this is a sign that blood is pooling). The arterial picture is the opposite: a foot that is cool to the touch, pale or blue, with pain that may go away when the leg is dangled down.
One general benchmark applies whatever the cause. A wound is called non-healing if it has not started to heal in 2 weeks or has not completely healed in 6 weeks. A shin wound that has passed either mark is worth a proper look, whether or not it seems infected right now.