Again, my advice goes against the grain, but I'll argue that arch support is one of the central causes of PF in the first place. Other causes are obesity (too heavy for your feet to support your weight) and heel strike running (due to shock absorbing footwear).
Obviously, you need to allow the initial injury to heal and you do that by staying off your feet as much as possible, icing etc. Get a Lacrosse Ball (much more firm than a tennis ball) and really work that area of the foot. Once the injury heals, I suggest working on strengthening the foot back up to full strength and, at that stage, wearing arch supported shoes is only going to keep the foot weak. Following mainstream advice, I suffered through on and off pain for about 10 years. When I first got PF, I was running high volume miles while wearing shock absorbing, arch supported running shoes. I figured my running days were over for good during that 10 year window of on and off again pain. Since I have gotten my feet back up to full strength going barefoot and wearing minimalist shoes, I have 0 problems running and run regularly. Though I have no interest to returning to high volume miles, I would have no hesitation about my feet if I felt inclined to sign up for a marathon or a ultra race.
I hate to say, but the medical community has a lot to gain by pain management (office visits, treatment, medications) and little to gain from recovery. In fact, many people with PF will tell you that full recovery is not an option. I struggled with it 10 for years before I figured out how to make a full recovery, but once I committed to the process of letting my feet do what millions of years of evolution designed them to do, recovery was pretty quick.