This is a domestic rabbit, it was someone's pet it, has been released in the wild to die a long painful death. Even in areas where the European rabbit are native, if it looks domestic, it is a released pet.
The 'pustules' are difficult to see clearly in the image, but the one on the ear may be a tick. The rabbit needs urgent medical attention, if you can take them to a vet today that would be great! Alternately contact a local animal shelter or rabbit rescue.
Not all animal shelters take domestic rabbits, if yours doesn't, or if they will not come out and pick it up. Check https://rabbit.org/ for your nearest rabbit rescue, not every rabbit rescue is listed at rabbit.org if the nearest listed is far away from you, contact them for info about one closer to you.
Updates after edits and other posts by OP.
From your description of interacting with the bunny, it lets you get close enough to spray meds on it's ears, but is not ready for you touch it yet. There are a couple of references above with help for catching a skittish pet bunny.
The longer he/she stays free the more likely he/she will die. A loose pet rabbit is not 'Free' it is 'Food'. Unlike Cats, domestic rabbits do not have long periods getting over being feral, they re-domesticate very quickly. If it is truly a released pet then the sooner you can capture it the better.
Rabbits are very territorial. It is likely it will stay in the same general area. They will be more active during the early morning and late evening (Dawn and Dusk). I am guessing from the photos that the rabbit is near a walking path. I suggest using a live animal trap as pictured below, you have been feeding treats for a couple of days now. Start putting the treats in the trap, in the same place. These traps can often be borrowed from local rescues, or purchased relatively cheaply. It is best if you can stay in the area of the trap while waiting for the bunny. If you don't catch it in the morning leave the treats, take the trap and come back in the evening to try again.