Does sound like classic PF. Start sleeping in something that keeps it stretched. Do some stretching and toe pointing, while still in bed to get it ready each morning for bearing weight. These measures will help prevent it from tearing each time you get up in the morning and put weight on your feet. Put some insoles in your shoes to keep the arch more flexed. Do a bunch of toe pointing exercises as soon as it can take the strain.

PF can take a while to get over. The faster you get serious about getting the healing started, the sooner it's going to heal. Where folks go wrong is that it can take them months before they get desperate enough to do the above steps. As a result, the healing they managed last night gets damaged each morning.

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Unfortunately, I seem to be the overlord of PF as I try all kinds of things to recover it. Since you just got it, the critical thing to do right now is stop all training until all the pain goes away.

Things to look for is running too many hills, cleats too far forward (move them way back) on your bike shoes, Running shoes old, floppy, lost arch support.

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Sounds like PF. I had it twice, once in each foot. Rest for 2-3 weeks. That means no running at all. You'll be able to bike pain free in just a few days if you knock it off with running. Then start running carefully. 10 minutes. Then 15. Stop if it hurts.

Rest works. If you want a quicker recovery, and of course you do, freeze a water bottle, and roll the arch of your foot on the water bottle for 20 minutes every day. Idea is to combine icing with rolling therapy. Another trick is to use your toes to pickup objects while sitting. Something the size of a dry erase marker works great. Or place a towel or cloth under your feet and use the toes to bunch up the towel and pick it up. To strengthen those muscles. Another idea is to take your shoes off while sitting and use a wall or edge of the desk or similar surface to stretch your toes upwards. (Google strassburg sock. They essentially do the same stretch for you while you sleep.)

One last piece of advice. If PF developed due to repetitive stress from piling on miles then you are good to go with rest and PT. If there is an underlying cause then you need to find and eliminate that cause. For me the 1st time the cause was a misshapen shoe insole pressing on my arch. Had to fix that insole to eliminate the problem. 2nd time was just bad luck and rest + PT fixed it pretty quickly. Did you change anything lately? New shoes? New socks? New insoles?