It can. Increased pain is one of the standard signs of infection. Redness, increased pain, or yellow or green pus, or excessive clear fluid around the injury are signs of infection. Pain that gets worse is a sign of infection too, alongside redness, swelling, pus or bleeding from the wound, fever and chills.
The same holds for specific kinds of wounds. For diabetic foot ulcers, increased pain sits with redness, increased warmth or swelling, extra drainage, pus, odor, fever or chills, and increased firmness around the wound. For ischemic ulcers, increased pain sits with redness, increased warmth or swelling, drainage that is yellowish or cloudy, bleeding, odor, and fever or chills.
The key word in all of them is increased. These signs describe pain that is getting worse, not pain that exists. A wound that has hurt since the day it happened and is slowly settling is different from one that was improving and has started to hurt more.
Pain is also always one item among several. Pain by itself isn’t treated as proof of infection, and there’s no simple way to tell infected pain from any other kind. With a wet-to-dry dressing, more pain is one of a set of changes to report — with worsening redness, swelling, bleeding, a wound that is larger or deeper, increasing drainage, and drainage with a bad smell — rather than singled out.
So the practical answer is narrower than the question. Worsening pain is a reason to make contact. It is not a diagnosis you can make at home, and it is most useful to whoever examines you when you can say what else changed at the same time.