Why does my baby pigeon have a red spot around its eye?

This looks like Pigeon pox, some birds recover from the disease spontaneously others don't but there is no treatment for it (not dangerous to humans). Pigeon pox is a viral disease to which pigeons are susceptible. Pigeon pox is caused by a virus that is spread by mosquitoes and dirty water but not in droppings. The disease causes pox scabs to form around the bird's face, mouth and feet.

If the baby's parents are still caring for it it is best to just leave it alone, especially if the bird is still acting normally. If you see any signs of illness such as lethargy, stumbling around, etc, it is best to contact a local wildlife rescue as this is a wild bird and they will best know how to care for it safely.

It would be best to try and bring the bird to your vet ASAP to have it treated as the eye and beak both look like there may be a pox or other sort of infection irritating it. You can use a clean washcloth to remove any debris from the eye to help keep it open and more comfortable. Making sure to keep the bird away from any other pets or people is also a good idea to prevent the spread of any illness until it can be treated by your vet.

It looks like the pigeon's ear may be a bit inflamed or there is some sort of growth/infection present. If they are wild birds, it would be best to contact a local wildlife rescue or animal control in your area so they can safely capture, examine, and treat the birds before releasing them back into the wild.

I would be very careful about cutting it off as there are a few skin infections that birds get which could do damge to the skin if cut. I would persevere with bathing it, and if it will not come away I would have an avian vet look at it as it is likely an infection that needs treatment.

Make sure there is nothing caught around the toe that could be causing constriction, if so remove it. It looks like the claw could be infected so you would need to take the pigeon to the vet and clean the toe with chlorhexidine whilst administering antibiotics such as baytril or terramycin.

Possible causes for a white appearance in the oral cavity could include thrush (a candida or yeast infection) or trichomoniasis (a parasite). Both of these conditions require veterinary exam to diagnose and treat, so a visit to your veterinarian is needed.