Since you have already had it cultured and it tested negative, I wouldn't worry too much (at least not yet). My daughter, now 21-months old, started having the same problems at about 16-months. It took close to 6-8 weeks before it seemed completely resolved (although we had days of no problems, it would come right back).
The absolute first thing our doctor has always done with vomitting and/or diarrhea is STOP ALL MILK PRODUCTS and other regular diet items. Give Pedialyte, Gatorades, Propel, Water, Flavored Water, Kool-Aid, weak tea, and if you must, flat soda. I personally don't recommend the flat soda, especially for vomitting, because it has always tasted so nasty to me that I don't give it to my kids. I also don't give my daughter soda although Sprite or Ginger Ale wouldn't be too bad. This is why:
Even without a milk allergy but proteins from dairy is harder to digest than others and can do two things, if you are fine and have too much you can become constipated. If you have any kind of "stomach bug", virus, or irritation you can get diarrhea. Even though you are better, it can just be a bit to hard to digest.
My advice would be to follow the following instructions, this is what our pediatrician has us do:
Day One - stop regular diet and all milk products, give the liquids I named above. The idea is stop everything but keep them hydrated. If they can tolerate it, JELLO is ok (not pudding). Avoid fruit juices!
Day Two - continue liquids, add bananas, peaches, and pears (baby food variety of these are ok too regardless of their age)
Day Three - continue above and add vegetables (again, baby food is ok)
Day Four - continue above and add meats (again, baby food is ok although older kids will bulk at it but don't give anything too greasy)
Day Five - Regular diet except milk products
Day Six - Continue above, add cereals (no milk yet)
Day Seven - Continue above, add milk (*you may want to add it slowly, like a serving or two at first and/or try soy milk or lactose-free milk for a week or two and wean back to whole or 2% milk).
On day two, do not add applesauce as it can contribute to loose stools as can fruit juices (especially apple juice). This is because of the sugar (natural and/or added).
Sometimes with my son, as he got older, I found that he may want or need the fruits and vegetables before they are scheduled especially if diarrhea was the problem (with vomitting, he didn't want them early).
With my daughter, we wouldn't get to day seven before the diarrhea would return. Then we would start over, get to day seven, and a day or two later it would start again. We stopped everything again. At day seven, we slowly started lactose-free milk (both for drinking and to prepare items that normally require milk). Once she was good for about two full weeks of being back on milk products, we gave her some whole milk again (slowly). After a week or two on both, she went back to whole milk and has been fine.
I hope this helps. Good luck.