when sprinting up that hill your foot is forced into dorsi-flexion much more than normal. There are several bones and multiple joints in the ankle - If you stepped hard and slightly awkwardly (uneven ground on the hill?) you may have 'jammed' one (or more) of these joints. May not necessarily be that painful at the time.
Because you are obviously relatively fit and strong your body is able to compensate for this subtle loss of movement most of the time. But it will be inefficient as muscles will have to work harder to compensate ("feel weak"). Muscle are fine so won't show up on muscle tests. If bones are jammed you may experience pain from time to time but sounds like any irritation heals/subsides relatively quickly.
IF it is the above manual therapy of the joints in your ankle should resolve problem. Hope physio you are seeing is experienced sports/running physio who should be able to do that.
They are unusual symptoms! Try to see a sports doc or one who runs him/herself. otherwise the normal story is - Patient - "It hurts when i run!" GP - "Well don't run then"
Does your knee literally seize up when you stop running and get the pain? If so it could be meniscus or cartilage damage - definitely need a referral. If not... is it when you fully straighten your leg that you get the pain? If so, maybe muscle imbalance causing the knee to twist awkwardly. The knee is not just a hinge joint - it does need to twist in and out slightly to work properly.
Muscle imbalances probably down faulty biomechanics when you run. Your joints will only put up with that for so long before starting to complain! The other knee probably starting to hurt because you're walking awkwardly to compensate.
There is a lot of conflicting information on the web because there is no one-size-fits-all solution unfortunately. The most important thing is the shoes you wear feel comfortable to run in.
There is also conflicting evidence for orthotics and arch supports and PF - They work for some people and not for others.
You could try changing gait by running with shorter stride if you are heavily heel striking - may/may not help.
If you are new to running (less than a year) i would go down a more supportive shoe route as your foot/leg muscles may not be strong enough yet.
If you're new to running or not - calf & foot stretching is the most powerful treatment you can give yourself for PF.
Try stretching your calves 4 different ways as they target different muscles in your calf that maybe contributing to stubborn PF.
3 - 4 times per day for 1 minute each time: 1) straight knee, 2) bent knee, 3) toe flexors (bent knee stretch with toes bent up against a step/wall and 4) inside calf stretch (bent knee with inside of foot dropped off edge of step (outside of foot on ledge)). You might feel one stretch more than another so hold that longer. Need to persevere for at least a week, 3/4 times a day. Relax into a moderate stretch, shouldnt hurt to hold stretch.
The trainers you wear are only a part of the 'big-picture' of your running. Do you feel comfortable running in the new trainers (before knee started hurting)? If they did then i 'd look else for the problem - possibly your running gait, maybe an issue with your calves/thighs/hips/back being tight/weak. Knees joints can be the 'weak link in the chain', but doesnt mean they are not built for running.
Feet are supposed to pronate, more so when you run - it is a natural suspension mechanism to absorb shock. Current scientifc thought is there is NO such thing as over-pronation (doesnt seem to have filtered thru to most running shops yet) - more likely the speed at which your foot pronates is too quick or they dont supinate (come out of pronation) quickly enough when you are running.
Id always reccommned you bit bullet and to see a sports physio who has experience with running injuries. At very least i would try stretching - calfs/quads/hamstrings/gluts and I would also try some calf and hip muscle strengthening exercies - but dont quote me on that because i havent seen you!
It sounds like the impact is damaging the calf. You should do swimming/more cycling instead as that will work the calves without as much impact. You could try building up strength in the calves by doing calf raises for a week or two, and start incorporating running - but only 2 x 10min runs p/day, and slowly build up the time running if you get no reaction.