If I am wearing Tefilin, and I feel very thirsty, should I take off my Tefllin to drink, (if I am even allowed to interrupt) or am I allowed to drink water while wearing Tefilin?
The Shulchan Aruch (OC 40:8) rules that אכילת עראי temporary eating is permitted while wearing Tefillin. Drinking water would seem to fall in this category.
In Yerushalmi Ber. 22b two Beraisos are mentioned concerning the t'fillin blessing, one says once (אית תניי תני מברך םעם אחת) and the latter twice (אית תניי תני פעמיים) a day.
A large meal while wearing t'fillin (הא אכל ואינון עילוי) would be considered an interruption that diverts attention from t'fillin and thus requires the blessing to be repeated, as referred to the latter Beraisa.
According to Rabbi Z'eira Rabbi bar Yirmiyah interpreted the first Beraisa as referring to a snack (עראי) which does not constitute an interruption.
Nor does a glass of water, we may suppose...
In the sefer Minhagei Chasam Sofer (ס'א) it is written that the Chasam Sofer's custom was to learn with his teffilin on, and while he was learning he had coffee brought to him, and he would drink.
וזהו לפי מנהגם שהלכו כל היום בתפילין, ולא לדידן. ונראה לי דלדידן לא נכון גם אכילת עראי בתפילין
This is according to their custom that they went the whole day in Tefillin, but we don't do this. And it appears to me that according to our custom it is not proper to eat temporary eating wearing Tefilin.
Although your case is more mitigated (very thirsty, only water and the disruptive nature of removing Tefilin for just that purpose) rather than the blanket permission the Aruch HaShulchan was addressing.