I'd not heard of this condition until I read your op, however, I'd never heard of an inflamed Psoas muscle either until I developed one.
Please just let me explain a little about mine first.
The Psoas muscle arises from the spine, passes through the pelvic girdle and attaches to the upper thigh bone. There is one each side of the spine, and passes very close over the sciatic nerve.
Mine has been caused by too much sitting down causing pressure onto the sciatic, to the point where I was being woken early in the morning by pain that made me scream out loud, and like the info you read about yours, I didn't read that the pain could be that bad either. But then, the text books don't want to scare anyone unduly - do they!
Your pain is triggered by walking - mine by sitting - the irony is ....deafening, is it not, op? and please, please know you have my full understanding and sympathy, it's beyond awful.
Mine started late last year, and I stuck it out until going to see a fabulous osteo earlier this year, who gave two treatments close together, and then a set of exercises, interspersed with monthly follow up treatments. Now, 6 months later, with short exercise sets each morning and night, and a walk every day if I can manage to, I'm fine.
So now you Op. I'm not a Doc, but can only speak from what I've experienced.
Heat, massage and stretching sounds good, so keep doing it.I use those in various amounts throughout the week in addition to my exercises to help keep my muscles/joints loose.
A big YES to the exercises. I would say it took a couple of weeks before I could sit down with bearable pain, and three or more months before I had no pain at all. I also still see the osteo once a month as a maintenance thing. I also know that If I stop walking/exercising it will return. So stick with them, even if there seems to be no improvement to begin with. Painkillers helped me too.
My decision to not see my doc over my problem and to go straight to the osteo, is because I would have just been sent to a physio anyway, so I cut out the middle man. The choice as to whether you go see one or not is yours .
I really hope you can sort this.