When you have green snot does it go away on its own or is that a sinus infection and need antibiotics?

To better and more . Accurately assess what it could be, you will need to go see your doctor for an evaluation. He/she will ask you a few questions, like any headaches, fevers, chills, nausea, vomiting, productive cough, post-nasal drip, excess mucus production, itchy runny nose, sneezing, itchy eyes, ears, and throat, ;nasal congestion, etc. Then he/she will examine you. Don't take antibiotics if you don't need to.
Snot's not enough. Most cases of sinusitis should not be treated with antibiotics. The exceptions are those cases that are particularly severe or prolonged. Green or yellow snot is a fairly standard aspect of having a cold, and not in itself an reason to take antibiotics.