Swollen lymph nodes usually occur in response to a bacterial or viral infection. Hence you may be having the swollen lymph nodes in response to the cold. For the weeping rash it can be an abscess, boil or impetigo.
Imeptigo is a highly contagious superficial bacterial skin infection. Primarily caused by Staphylococcus aureus and sometimes by Streptococcus pyogenes. Topical and oral antibiotics are the treatment of choice. My sincere advice would be to consult a dermatologist and get a culture sensitivity of the discharge and if staph is confirmed then get prescribed oral antibiotics also because sometimes topical therapy with antibiotic creams is not sufficient for the treatment.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.