Ironically, while there was no pop, I did pull my calf playing badminton a few weeks ago. For me, I nabbed some paracetamol or general pain killers and let it heal up on its own as I could walk on it but very slowly to begin.
For you though, it sounds like a possible tear based on the part in bold, especially as you can't put pressure on it. A mate of mine did something similar a few months back and was on crutches for a couple of weeks, so I'd give the doctors a buzz asap.