Your symptoms sound so similar to mine- but one thing, not sure if its the inside or outside of your calf. For me my pain was all on the inside of my calf (or otherwise known as the posterior).
I would advise first googling "posterior tibial pain" to see if we are talking about the same things.
The first time I had this pain on the right leg it was after boosting up my training and pushing things maybe too far. Also getting a new and perhaps ill fitting pair of trainers from TK Maxx which were probably old and the cushioning depleted as they do when they are kept in storeage.
I tried to ignore it, it got worse. Someone advised rice and massage so I tried, it turned into a long bruise which faded after a week but looked odd, caused more pain so I didn't try this again. Instead I saw a doctor who couldn't work out what it was, sent me for an xray, said it was not a fracture and I assumed I must be being OTT so I kept on running and tried to run through the pain. I worked out that any impact bar walking at a snails pace hurt like hell. A physio I saw was also clueless, asked me to hop to build up muscle to help but offered no diagnosis and no real solution.
It got to the point where I could only run for 1-5 mins and then had to stop, catch my pain threshold and then restart again. Luckily by chance I sprained my ankle, I stopped running for a good few months. I did other forms of exercise as I couldn't take any impact without pain. I bought a new pair of trainers (same model as before just newer) and began to run again= no pain!
I then assumed I was cured, kept on running and was so happy! Then Xmas came and I went running in the snow, completely changed the way I ran so as not to slip. I only did half an hour, went home spent the rest of Xmas day walking from family member to family member in non supportive footwear, didn't rest as I should have done, didn't even warm up before my run.
I went back to the gym and the pain had returned but in the other leg, I researched into it a bit this time and worked out I had posterial tibial pain, caused by....fallen arches!
I have been refered to a different physio this time, she guessed it straight off! Taped me up, showed me the muscle in my feet was not even present- the arches had fallen and I had to get the muscle in the tibia which had been yanked on by the arches collapsing, to repair and then build up the muscle in the arch so the tibial would not be yanked on again.
I was recommended a pair of orthopedic insoles which I have too see an orthopedic person about next week (waiting list was long!) but you can get these privatly for around £30 from a physio too if you have the money. I am told they will release the pressure on the tibia so it can repair better.
I was also told to go back to running slowly, I used to do 60-90minute shots and have been told 1-5 mins at a time max and build up slowly. Not happy about that but am happy I have an understanding of what the problem is so I can go back running.
Its maybe an idea to see if you can speak to a physio, see what they say. It could be shin splints- where the muscle comes away from the bone or tears at it like what I maybe had or was edging on and this can eventually cause a stress fracture which you don't want as these will take longer to repair and could prevent you from not just running.