I'm not sure but is green tea unhealthy for you?

No. It is generally : Healthy. However a significant overdose of green tea (usually extract) may lead to irritability, insomnia, irregular or rapid heart rate, muscle twitching, nausea, vomiting, diarrhea, abdominal cramps, liver damage, trouble breathing, dizziness, fever, confusion, hallucinations, diuresis, seizures, loss of consciousness ; even death.