Working through a flat-foot caused knee injury

Good morning! This weekend I went camping with my husband. We were carrying very heavy packs and it was a steep hike. I think it was going down that did the damage. I have very flat feet--the part of my foot where the arches should be sits flat on the ground. I wear birkenstocks around the house and try to get workout shoes with good arch support, but it's never quite enough. My flat feet wear the arches down right away. So I think my hiking boots weren't offering enough support, and the added weight from my pack put too much strain on the medial region of my knee. I don't know exactly what is wrong, but I know there is an injury. Both knees are tender to the touch almost as though they are bruised on the inner side of my knees just below the knee cap. When I tried to do the elliptical the other day, the pain radiated up into my thigh, and felt almost like a cramp. Yesterday I took the day off, but felt very sore walking my dog.

I don't want to lose weeks in the gym over this. My question is, do any of you have flat feet and resulting knee problems? What are some strategies to manage it, besides using inserts in your shoes? Do you use a knee brace? Do you ice? Or do you just have to quit straining it entirely by staying out of the gym for awhile? I use the elliptical to avoid high impact, and I really don't want to have to stop. Any advice would be greatly appreciated. Thank you!