In the end, it takes but a few seconds before you reach your decision: no, you will not drink the girl's milk, for several reasons. Unfortunately, that means that you just refused to act on the one way to get rid of the stuff.

Yet you don't have any regrets: sure, now you will have a harder time finding a comfortable spot to sleep, yet in your mind that's preferable to drinking the stuff. 

So, with no better alternative, you just find the best possible position, out of risk of a potential drowning, before remaining still: if you want to take advantage of the girl currently being mostly asleep, you would want at least to have as much space of action as possible, something currently unavailable due to the presence of milk in your "room".

However unintentional, your actions got noticed by Shina, who now in a more awakened tone, asks confused:

"Why...why is he still? Come on...little pet...drink it...it's nice and tasty...please...It would make me very happy to...feel you drinking..."

Well, now you're again at a crossroads: the girl who is now but a step away from full consciousness expects that you drink her milk. Perhaps that is now reason enough to drink the stuff if just to calm her? Or despite that request of hers, you remain unshakable on your current defiance against such a proposition?