There's a medical saying: "When you hear hoofbeats, think of horses, not zebras".
I know you are worried about your kiddo, but LOTS of ordinary things cause nausea and vomiting in children (and adults). As you've probably noticed, most people who throw up do *not* have brain tumors.
If you've noticed one of your child's eyes going off-axis, well, that can affect eyesight in a youngster, so take him to the doctor soon for a workup. By all means, report the throw-up, and if you're still worried about brain tumors, mention that also and the doc will take it from there.
But really, don't waste a lot of time fretting about a rare occurrence (and one that usually causes other symptoms as well). Just take care of business and get your little guy's eyes checked.
I think you should make an appointment with an opthamologist or a developmental optician to have the eye looked at, and worry about a brain tumor only if a medical person suggests you should. Kids' eyes turn inward for other reasons, and he is a good age to begin eye exercises if the eye moving inward has come from something that exercise will fix. I assume an eye specialist would be able to tell you if a brain tumor is even in the realm of possibility for your child.