It's good to hear the calf nursed.
The thing is, this cow's udder will not improve with age. If she were my cow, I would send her down the road after she gets done raising this calf. If the calf is a heifer, I would not keep her as a replacement either.
Bad udders are highly heritable trait. Life is just too short to mess with stuff like that.
As to vaccines this newborn calf should have. The calf should get a 7-way clostridial shot, and a booster shot in 6-8. If weeks.
If there are horns, now would be a good time to take them off with a small scoop, dehorning paste, or hot iron.
If the calf is a bull that needs to be castrated, now is the time when rubber bands work the best, or simply knife cut.
Be sure to watch out for flies this time of year. An aerosol wound spray around the horn and scrotal area might be beneficial.
The blackleg vaccine can be given at any time. I'd wait a week or two until the calf is nursing well before doing the stressful horn and castration jobs.