My kid had ear infections (not tons, but a few) when he was little, and we'd get prescribed amoxicilin (if memory serves, it may not...) which as I recall was the dosing/frequency you describe. Like your LO, mine would vomit it up (no sensory issues or anything in our case, he just didn't like it, already didn't feel good, and reacted to having yucky-tasting liquid effectively forced down his throat. Go figure.).
Somewhere in navigating that, I learned (because we went back to the pediatrician to get help and this was the solution provided) that an equally effective treatment (I think ... I'm not a doctor) is Zithromax given once a day for 5 days.
Obviously that doesn't 100% eliminate the problem, but it does reduce it. Zithromax is (I think) broader spectrum and something they try not to use as a first line of defense but -- if you can't get the medicine in the kid, it's not going to work, so ...