A snotty nose is caused by irritation of the nasal sinuses and passages. Nasal botts, a maggot of the bott fly, Oestrus ovis, is often the cause. If there is more than a month before sale time, use Ivermec drench to treat. Contact your leader or veterinarian to obtain the drug. If the Ivermec does not help, give a long acting tetracycline as described above.
If this condition occurs after the first part of August and the lamb is droopy, his temperature is over 104, and it does not respond to the long acting tetracycline, your lamb probably had Bluetongue, a viral disease. In addition to the snotty nose and depression, the lamb may be stiff and reluctant to get up and it may also have diarrhea. It's face and ears may get puffy, and it may drool due to sores in its mouth.
Viruses do not respond to antibiotics, but the antibiotics should help to prevent pneumonia caused by opportunist organisms. Keep your lamb as comfortable as possible. Be sure it has shade. Clean its nose occasionally to help it breathe. Give 1 aspirin twice a day and be sure water is nearby.
Spray the premises and your lamb with a fly spray that is labeled safe for livestock.