Hi - a diagnosis is key so pursue that ASAP so that you know what you're dealing with
That said, I did non-medication approaches with my oldest son, who was diagnosed with ADHD-inattentive at age 7. I was very wary of medication and while his ADHD was a struggle for him and annoying at home, he didn't have behavior problems at school and was fairly compliant. He was also receiving accommodations at school under an IEP due to learning disabilities.
For a while, when I had more control of his diet, he ate optimally. Under the guidance of a chiropractor who practiced applied kinestheology (muscle response testing), he was on a cocktail of supplements to support his adrenal function, calm his nervous system, etc. Lots of products from Standard Process, and with appointments and supplements, I was spending about $400 a month out of pocket, which was unsustainable in the long term. He was less agitated and more pleasant when we kept with this regimen. I also had him complete about half of a full course of a treatment called Brain Integration Technique (BIT) in middle school. We stopped because I couldn't afford it anymore and it took up a ton of time for session appointments. I hadn't said anything to the school about the BIT program but spontaneously, his SPED teacher and another teacher reached out to ask if anything had changed at home because he seemed much more focused and was doing noticeably better at school. I really wanted him to do some "alternative" therapies at a well-known center near us (The Hallowell Center in MA) but it was $5K and not covered by insurance just for an initial workup, so we were never able to have him seen there. He also took Juice Plus products in high school and felt that those helped him feel better. With all that time and money, none of this was terribly effective and it was a lot of effort, time and money for unremarkable results.
In high school, he tried various ADHD medications but the side effects were intolerable for him even at the lowest doses - chronic headaches, severe insomnia (sleeping 1-2 hours or not at all), not eating, rapid and uncontrollable chatter, severe irritability and rage as it wore off, etc. We tried several different medications and the longest he used one was for 6 months. It was not a magic cure for him, but he still considers going back on (he's 19 now). I hope he can find one that suits him.
All that said, medication has been a miracle for my 13 year old. He was diagnosed with ADHD combined type two years ago and his behavior was so problematic and such an issue for everyone around him that it would have been unconscionable to not try medication along with counseling and accommodations in school. He was just a different kid with a very different case. Initially, he didn't feel any effects of the medication at the lowest dose but he tolerated it well. After two dosage increases, it was night and day for him. He doesn't like himself when he's not on his meds - he worries that he'll zone out, start talking about things no one cares about, and annoy his friends. That dose started wearing off before the end of the school day so we just increased it in the hope that he'll be able to sustain focus long enough after school to do his work. His only side effects are that he can't fall asleep for 14 hours after he takes it and he's not hungry for about 12-13 hours, so he doesn't each much during the day, inhales food from 8-9 PM and then goes to bed.
Obviously if ADHD is an issue, you can't try medication until he's diagnosed. If you're interested in alternative approaches as you work through the diagnosis process and have the time and money to invest in seeing someone, I would find a naturopath in your area so that instead of just buying expensive supplements and throwing at the wall and seeing what sticks, you have someone who can make recommendations based on his diet and needs and can evaluate whether or not things are helping him. The DIY method can be a tremendous waste of time and money but with someone who knows what they're doing, optimizing nutrition through diet and supplements really can improve health and perhaps address some if his symptoms.