I'm just guessing here and I'm by no means an expert.
The water and gasping I think would be down to the drug making you very dehydrated, an overdose of any barbiturate and you're going to have that dry mouth feeling.
The coughing and gasping I'm fairly certain to a degree that he would have been so far into nodding off that it would have cause him any real discomfort, look at the rest of his body, he isn't fighting or thrashing. When your mouth becomes so dry from overdose (speaking from experience) it can feel like you have hairs on your tongue or in the back of your throat so may cause some coughing, desire to drink water.
I think he slipped so quickly into unconsciousness that we can agree that even if there was discomfort (there's a difference between discomfort and pain, I don't believe he was in any type of pain) then it was minimal and lasted literally seconds.
From my own recent overdose attempt, I had moments of consciousness in the ambulance and hospital where I can remember saying I couldn't breath and I was struggling/panicked but it caused me no pain and the comfort was minor if anything and I kept quickly sliding into unconsciousness again. That attempt hasn't left me not wanting to do it again because the discomfort was so minimal.
I can't draw a direct comparison and I suppose this can be debated day and night on here and nobody will ever know apart from Peter but my guess is he didn't experience any great deal of distress from this and he passed peacefully.