yagi jal deureoseo jigeumeun byeongwone dasi gal piryoga eobsdaeyo.

Not literally. In this sentence, 들다 means to take effect / to work, not just to enter.

So 약이 잘 들다 is a common expression meaning:

• the medicine works well
• the medicine is effective
• the medicine is taking effect well

So 약이 잘 들어서 means because the medicine is working well or since the medicine has been effective.

Because the medicine is the subject of the verb 들다 here.

In English, we often say:

• The medicine is working
• The medicine helped

Korean does the same kind of thing here, so the medicine is marked with 이/가:

• 약이 잘 들다 = the medicine works well

If you used 약을, it would suggest the medicine is the object of some action, which is not what is happening in this sentence.

잘 means well.

So:

• 약이 들다 = the medicine works / takes effect
• 약이 잘 들다 = the medicine works well

It adds the idea that the medicine is effective, not just that it has some effect.