I am not medically qualified at all, just an old pilgrim who has seen a bit. With the "I am not medically qualified" warning, it sounds to me like it might be tendonitis. Inflammation and swelling of the tendons. If the shoes are not offering much support, it might be the result of too much twisting and turning. Tendonitis can be caused by an external irritant, like too tight laces or shoes or boots that are putting pressure on a tendon, or pulling the feet the wrong way, but also it can be from simple overuse. I met one fellow who was struck down at Carrion de los Condes, after walking quite happily all the way from Le Puy.
If it is tendonitis - your companion can try a number of things. Rest, elevation, ice (not compression imo).
Give trekking sticks a go, if not already using them. A change of shoes. Or try the stiff orthotic inserts one can buy from chemist shops - sold generally for plantar fasciitis but can also help with tendonitis because they stabilise the foot. Or try sandals for a while. Obviously try to eliminate any rubbing on the top of the foot if the problem is localised there.
For tendonitis I'm not a fan of feet exercises or deep massage when tendonitis is suspected, because sometimes that can actually exacerbate the problem. Well, it did for me.
And, as everyone says, don't keep pushing through the pain. A bit is ok, permanent damage is not. Get professional help if it does not clear - lots of physiotherapists and GPs on the route.