Question:
If one breaks their fast on Tisha B'av because they have a really bad headache or are feeling sick. Is there any merit in drinking water only and carry on fasting?
Answer:
The poskim say that one would not have to make havdalah befoe drinking, but not that it helps regarding the fasting aspect.
Have an easy and meaningful fast
Sources:
Shevet Halevi 8-129 (3).