I think it depends on your work. I broke my leg back in January and the physio told me that around 3 months off work was to be expected. BUT, if you have any sort of physical job that could make it harder to return. I'm a teacher, and although many people were surprised, I did manage to get in (on limited duties and then a phased return) after about 2 months, but only because I had adult support in class and a reliable crew of people willing to give me lifts to and from school.
But if I worked in, say London, and needed to walk to the station and commute in and deal with the tube and so on, I don't think I'd even be back now, nearly 4 months on - although I'm not sure whether not being able to travel there would count as a reason to be off work.
The bottom line is, if you've been signed off work by your GP, then you're not fit to be there, so they're going to have to suck it up.
I think it depends on the type of sprain and the severity of the break. I've been staggered by the impact of this (particularly bad) break, BUT I've been assured that I will (or should) make a complete recovery. Eventually. Whereas dh, who's had numerous twists/sprains/damaged ligaments and so forth, is probably always going to be limping/wincing in pain at something or other.
I agree that it sounds as if you've overdone it. And for the sake of your long-term recovery, you need to take it carefully. No one's going to be handing out medals for your bravery at hobbling in to work. Put yourself first.