Having puked on numerous occasions and as a reuslt of numerous influences, I feel it is absolutely imperative that you address, in the sound, the cause of the puke -
now a simple stomach flu would initially be a quick rumble followed by the splatter of puke in he bowl
grrrrooooolspppllooosh.
the "I drank too much" puke would be a quick turnaround by the booze,
hrrughllspplooosh. Again, it's liquid so it will sploosh.
Eating your mom's meatloaf.
hrraugh, hrraugh, hraugh (please note the dry heaves as your body tries to forcibly eject the offending substance) hrrraaaauuuuugghhlll - splack (the hyphen represents the amount of time the said offending substance takes to get from your mouth to the floor. You missed the toilet, by the way)
Now cat hair is going to take multiple rasping dry heaves (hhrrssaaackll) followed by a short space then an exquisitely painful "Ack" which represents the last spasm, i.e.: hhrrrssaacckl - hhrrassaccklssl - hrrsackarrshack - - aaack!
Please don't inquire as to my personal experience with the cat hair. It's not a pretty story.