Do i need an antibiotic for consistent cough with green phlegm?

May be: but, to treat what? Bacterial sinusitis, bronchitis or pneumonia, maybe it is just viral, better get seen by your doctor / ENT specialist for assessment, what type of antibiotic and for how long, if needed, good luck

Almost certainly: It's actually a controversial area. There's "are you going to die from it" and that's thankfully rare unless someone has a lot of other health problems or over age 70. Then, there's will I have a better life from taking antibiotics. Again, controversial. First, we tend to forget to give anti-inflammatory respiratory meds (monteluekast, maybe inhalers)