This is sad, but i do understand the pain. We never understand a problem unless it affects us personally.
In my opinion in the first line while drinking fits, you could say alcohol is a better fit, because that seems to be the cause of problem within this poem. So to me it makes more sense to put it there. :).
Your poem is on point though, it flows nicely and it Doesn't stray off topic at all.
About the poem itself, i would say it is to be taken in literal sense, you are ssd about your dad and how much time he has left and it seems like alcohol is the poison that is destroying him. I don't think anything bad is meant to happen but it does a lot of time. You seem to feel surprised along with a deep sorrow because you care a lot and it was or seems to be an unknown thing that happened. Your dad has been drinking a long time so it seems and it finally caught up to him.
You are brave for writing. Hugs you tight xx excellent but sad write.