Like Dave, I don't treat every calf with a snotty nose, but if they start to act sick and I see them off by themselves and uninterested in nursing, we get on it fast. Your calf looks good in the pictures. I probably would not be giving antibiotics, but I would get her vaccinated.
A few years ago, we lost a calf to pneumonia. I had noticed him standing off from the other calves when we were checking cows one evening, but I wasn't too concerned. I figured I'd check him next time we checked cows and run him in the chute if he was still acting different. Well that was a big mistake. By the time we checked maybe 36 hours later he was off by himself and breathing rough. We ran him in the chute and gave him Nuflor and banamine, but we were too late to save him. Later I had another calf acting stand-offish, so we brought him in, took his temperature and treated him. He was better within 12 hours, but by then we had a half dozen more showing some signs of respiratory distress. We treated those, only to see more the next day. A veterinarian friend recommended we bring all the calves in and vaccinate them all with Inforce 3, an MLV intranasal respiratory vaccine that protects against respiratory disease caused by BRSV, IBR and PI3. He said to only give antibiotics like Nuflor or Draxin to calves with temperatures above 103. He works at a number of feedlots and that was part of their protocol. We did have to treat a few calves, but most just received a dose of Inforce 3. We never had to treat another calf after that.
We use to wait until calves were 5 or 6 months old to vaccinate, and we used all killed vaccines. This was mostly because it was kind of a pain to bring them in off grass and modified live vaccines made me nervous. Now we routinely give an MLV intranasal respiratory vaccine, a BVD MLV and an 8 way clostridial (plus booster) when the calves are about 2-4 months old, and we have not had any issues with respiratory problems since. You don't need a vet to give your calves these vaccines and they are pretty cheap. Our Coop sells Inforce 3 in boxes of 10, 25 or 50 doses, but we can even buy just a single dose for $2.30. There are other good intranasal vaccines, and some even include BVD protection. I would highly recommend you vaccinate all of your calves for respiratory issues. Ask your Vet or a good rancher to recommend a protocol for your area.