In this sentence,
dōu and you can't remove it.
Here are a few other similar sentences:
The two above sentences are similar, but they don't contain
得, so the person who speaks them is not unhappy about taking medicine, compared to the one in your question.
那段时间，他每天都会给我打电话 He used to call me every day during that period.
You can't remove
都 because it means you have to do this daily, and there is no exception. However, if there are a few exceptions, you may want to say:
I have to take medicine every day, but with a few exceptions (not particularly specified)
I have to take medicine every day unless that day my stomach feels very uncomfortable.