I’ve had massive issues with metatarsalgia over the last 5-10years. The single worst thing for setting it off was stiff winter boots, with or without crampons (although with crampons resulted in excruciating pain like two of my toes were on fire!!), also climbing shoes without a stiff enough sole.
I have dropped metatarsal heads which are largely genetic (or obesity related) by the time I saw a physio the arch of my foot was visibly higher even to the untrained eye. I know you said you can’t afford custom insoles at the moment, but the £230 i spent on the physio/ insoles was the best money I’ve spent in years, and worth forgoing a holiday for. I just left it and left it due to cost and being to busy and reached the point of struggling to walk some days.
Are you wearing them before you start running in them. Maybe your feet need time to get used to them if you aren’t a trainer wearer usually. Also you could try road race trainers. I have a pair of these think they are Peter Merrell. They were about 60 from Tiso and I really like them. They are a bit more like a walking shoe than a trainer.
I had trouble with an impingement last year-had a steroid shot and some physio, now have regular massages and its mostly behaving. Wearing a shoulder support whilst playing soccer and sports can help a lot. I wear this one shoulder support and it has really helped me especially when playing soccer.
I suffer in my right heel too and have found correct shoes helps me a lot. The Clarke’s Unstructured have been brilliant and I live in them. Not pretty but very comfy. Their summer sandals are good too.
If I wear anything else for a day it hurts like mad. Have to be careful with boots and when running.
I work in foot care product design and development
Ideally you need orthotic insoles, lots of anti inflammatory drugs and to relieve the acute pain get a really cold can of coke and stretch your arch over it regularly by rolling it backwards and forwards under your foot
If you haven’t already you need to see a podiatrist not just a GP!