My dad had a brain tumor and he never had a headache nor stomach pain/nausea. These symptoms are much more likely to indicate much more mundane issues. It is not uncommon for heat to bring on migraines with both nausea and headaches. Heat can even cause this in people who don't have migraines. Give him cold water to sip, have him rest in a dark room and he should recover just fine. I agree that you should set up an appointment with his regular doctor just to address your concerns and see if there is something you can do to help prevent it from happening again, but I do not think an ER visit will do any good (and may do more harm if it aggravates his HA).
Also, kids really pick up on our anxieties. I know it's hard, but try to be calm and reassuring when you're in his presence. He will pick up your anxiety and it will exacerbate his own HA. Headaches and nausea are both very common, and brain tumors truly are not. This will pass.