Hi Sarah, I've been suffering pretty much exactly the same with both my calf muscles. Just before they "clamp" i have a numbness, pins and needles feeling and then bang the pain is very deep in the soleus muscle. Really painful and frequently had to walk/hobble a few miles home.
Anyway after much searching i think it might be this "Chronic Exertional Compartment Syndrome"
Briefly muscle becomes enlarged and compressed not allowing proper blood flow to the calf. Ive yet to go to the Dr's as after 30yrs of running i generally sort myself out and I've never had a calf injury before. If you google CECS it might help.
I had the injection into the Bursa and it worked immediately tho i didn't run for 3 days. It felt great to run pain free but ....... it only masks the problem and does not cure it. After 6 months the pain gradually returned, i waited for about a year and had a second injection, this one lasted 3 months. I decided no more as i read that too much corticosteroid will eventually weaken the tendon and it has with me. Would i recommend it, I'm afraid not.
If you do go down the injection route, the injection has to be administered in exactly the right place so make sure its someone who knows what they are doing.
Good luck with what you decide on and your recovery.
You might find the following i/view helpful with Hakan Alfredson, a runner and well respected person in this field. If your Achilles pain is where it attaches to the heel bone then be careful it does not develop into Haglunds Deformity which can be a result of pain in this area. Hope you recover soon.