Green vomit means that bile is present.
This can also be yellow thru to dark brown.
Main question.
Are you in any pain? and if so whereabouts?
You are not killing yourself.
You will be very weak because this is the end product of vomiting.
Yes, I have heard of vomiting increasing over time but the main thing is you do not become dehydrated and where you are able to hold down some water.
The burning sensation is from discarded stomach acid.
Worrying will only serve to exacerbate the issue and make things worse.
If I were you I would still persevere, but if this continues beyond another 2 or 3 days then you will need to break the fast on diluted fresh juice and then only sipping gradually over time.