Go with you gut instincts! Find another Dr. & get another opinion.
What you're describing isn't normal, nor should your son suffer without some sort of follow up. Sounds like it's getting worse. Having his eyes checked was a good start, which I assume was normal. If it is allergies, he should be seen by an allergist to find out if & what's bothering him.
Are there changes going on @ home/school/daycare which may be stressing him. You wrote that you are a newly single mom, sounds like some ____@____.com world as he knew it may have changed and he doesn't know how to handle it. What may seem minor to you may be overwhelming for him. He see things through the eyes of a 5 yr old.
He maybe worried about you. Ask him if anything is bothering him. Maybe he's being bullied @ school/daycare/ friends that you're not aware of.
Make sure he's getting enough sleep and is eating well.
Try to watch what he eats. Keep a record of what he eats & when he has a HA. Look back over the last 24 hours and see if there is a common food. Watch for foods with preservatives or MSG in it. Limit sweets.
He's had these HA for too long without knowing the cause. If I was having frequent HA's without testing to find out why, you better believe I'd find a Dr. who would believe me.
I hope he feels better soon! Good luck!