Could be the start of pneumonia, or the BRSV which is a resp virus. DRY #1, and then warm. If it continues for more than 36-48 hours, call the vet. They will probably, hopefully, give you something like either Nuflor, or Baytril. Shot to be given under the skin (SQ). Calves can get very sick very quick. If you do not have an already existing relationship with the vet, then they may require a visit.
You can buy Penicillin and LA200 or LA300 (oxytet) over the counter. Different types of pen, I like the dura-pen type. I am not afraid to give a shot of pen for 2 or 3 days for something like that. Follow directions. I try to keep it around for any kind of problem as a precaution. As long as the calf is eating and drinking you should be okay. Staying hydrated is the biggest thing.
Is this your first calf? A couple of days with a cough, but no other symptoms is not the end of the world, but a cough can quickly "go south" so bears watching. You don't want them to get lung damage so better to err on the side of caution and treat, than let it go and they get worse and then will take more to respond to treatment.