Learn Turkish: Yeğenimin ilacını hemen içmesi lazımdı. - My nephew had to take his medicine immediately.

This is the core structure for past necessity. We use the short verbal noun içme (drinking) and add the third-person possessive -si to mean 'his drinking'. Then we add lazımdı (was necessary). Literally, it translates to 'his drinking was necessary'.

Why is there an -in at the end of yeğenimin?

That is the genitive (possessive) case. Because the action is 'his drinking' (içmesi), the person who must do the drinking takes the genitive case, just like a standard possessive phrase. So yeğenim (my nephew) becomes yeğenimin (my nephew's). The underlying grammar is literally 'my nephew's drinking'.

Break down the word ilacını. Why isn't it just ilaç?

First, the ç in ilaç changes to c because a vowel is added. We add the possessive -ı to mean 'his medicine' (ilacı). Then, because this specific medicine is the direct object of the verb, we need the accusative case -ı. The -n- is a buffer letter between the two suffixes: ilaç + ı + n + ı.

Why do we use a form of içmek (to drink) for medicine?