The difference between drinking lots of water and drinking lots of tea (whether green or black) is that tea, in addition to the liquid, also contains caffeine and other chemicals which are diuretics and will cause you to urinate more frequently. This is why you are noticing more urination with tea than you had previously with water.
If you cut back a bit on the tea, you should notice that the urination slows down. You haven't done any permanent damage to your bladder or urinary tract by drinking the tea and, in fact, if the frequent urination
doesn't bother you then there is no problem at all!
However, if you cut back on the tea and you notice that the urination still keeps going, then you should go see your primary care doctor
. Other reasons for frequent urination include an increase in the levels of sugar in the blood, which could be a sign of diabetes. Also, urinary tract infections and some sexually transmitted infections can cause frequent urination.
If things sort themselves out with simply cutting back on the tea, then there is nothing to worry
about, but always you should feel free to ask your primary care doctor about this and other general health questions.