Yes. It’s one of two situations where gloves are specifically called for: put on clean medical gloves if your wound is infected (red or oozing) or if you are changing the dressing for someone else.
That’s worth noticing, because gloves aren’t required every time someone changes a dressing on their own wound. Caring for someone else is one of the two situations that changes the answer.
They do not need to be sterile. Clean, non-sterile medical gloves are what’s used for closed surgical wounds, open surgical wounds and wet-to-dry dressings alike.
What matters more than the type is how often they’re changed. In a packed-wound dressing change, you use three separate pairs: one to remove the old dressing, a new pair to clean the wound, and another new pair to apply the new dressing, with hands washed in between each.
Gloves also don’t replace handwashing. You need both. Wash your hands before touching the dressing, again after the old dressing and gloves go into the bag, and again at the end.
The gloves protect in both directions. The direction that matters most here is this: your skin protects your body from germs, and when the skin is broken, germs can enter and cause infection.
If gloves aren’t available for a change, mention it to the clinic rather than quietly working around it. Supplies are something a wound service can usually help with.