Don't try to translate literally, it does not work all the time.
İlaç and iç does not have an etymological relationship. Medicine also means 'tıp', and here it is used with this meaning.
Here, iç hastalıkları (you can also see the word: 'dahiliye' meaning also 'iç hastalıkları') literally means the diseases of internals (internal organs). The only difference is we use the word 'disease', in English they use 'medicine'.
I hope it is clear :)
It means diseases. If you write "internal diseases" it will be accepted also....
It should be "Internal disease" because hastalık means- the condition of a persons siknessç Medicine means- ilaç