Is your foot/cleats and seat height in the same position as your road bike, I had a sore Achilles for a few years because of overuse walking hundreds of miles and it only came back on the bike when I had my cleats to far forward on my shoes, lowering the seat a few mm and pushing the cleats back on the shoes sorted it out straight away.
This is a good question; cleats are in the same position as I literally just swapped the pedals over. The frame is a different size though, i've gone from a B'Twin 58" to a Pinnacle 52". Both frames fit me fine but i do wonder if the seat height on the Pinnacle is pulling my tendon. Will lower it and give it a bash.
Do you stretch?
Seen a Physio perchance?
I've been out of the gym since the off about 3 weeks ago so i've been stretching less. I'm hoping to get back to light gym work this week. I was doing a good regimen of squats, core and lifts so was building up my leg strength with endurance/max squats. It could be that but i wont' know until i'm back doing full gym work.
I agree with
@Eddy. Also, a shoulder dislocation may have changed your riding position enough to cause pain. Work through the measurement process and see if it comes out the same.
http://wheel-easy.org.uk/uploads/documents/Bike Set Up 2017a.pdf might be a start.
The shoulder dislocation has resolved itself, thankfully. The off caused some weakening of the tendons around my rotator cuff and 'pop' out it came on certain movements - i took 5 days or so off the bike and let it heal up. I'm wearing a support around the joint as well so it should be in place and not causing issue. In some ways i'm using my shoulders more as i'm pulling out of junctions/traffic lights on the singlespeed.
The cure is to take it easy, i.e. stop stressing it by heaving on a singlespeed and get back to the lighter loads of a geared bike, rub on Ibuprofen gel three times a day and perhaps ice it as well with frozen peas.
The Ortho chap who saw me with the dislocating shoulder said to me "I'm a cyclist too. I'm going to tell you not to get back on the bike for at least 6 weeks but lets accept that that's not likely to happen". This advice is absolutely solid and sensible but, as the good bone fellow said, it's not likely to happen