I don't like to assume anything here so I wont but reading what you have written, it sounds identitcal to the symptoms I had- does it hurt on a spot or few spots when you press? (try lots of little presses with the side of your thumb running up and down the area on your calf) if you can pick up a single spot or few spots, does it move day to day or stay put?
I had what the physios though was me being pathetic, actually turned out to be quite a pronounced tibial stress fracture! It hurt to run, went away after about 5 mins then came shouting back at me 10 minutes later and much louder then before. The reason for this is the endorphines kick in when you begin to run and they hide the pain from the SF. But as you continue on the endorphines reduce a little and the SF gets that bit worse so it suddenly comes back to let you know you need to stop.
The best way to get this sorted medically is to go to your doctor and get a scan- and MRI may show something up but I had to get a nuclear bone scan done which is far more expensive and long and detailed, the doctor/specialist had wanted to do this (I really didn't want nuclear material put inside me, not even a little bit!) because my MRI had no results- there was apparently so much swelling they couldn't see anything at all. So by all means get a scan if thats what you feel you need but the advice will be the same whatever. Physio help is likely to be about building the muscles around the area so it doesn't take the strain so much. You may have strong calves but there are more to your calves and lower legs then the gasteronemus muscle! The only real thing you can do before that though is rest. If you eat well, take it easy and careful not to add any impact, it took me about 4-6 months to get over it in total and thats with the odd "but it feels fine this morning, I'm gonna go running..." (ending in tears). The more you rest, the more you keep your nutrition at an optimal level, the sooner you will recover.
The idea is that you should be able to hop on the sore leg 20 times without any pain but I've not actually done this myself. The SF has taught me to keep the impact off if possible and I have totally changed my running style to adapt for it. (barefoot style/mid foot/forefoot strike where I used to be a maximum support heel strike runner). It all seems to have helped as the SF did used to fade and then come back again but so far hasn't come back- even if it were to come back I'd still be sold on the barefoot thing, I've never had so many months without calf/shin pain!