How long until wrist heals?

I fell over onto my wrist 4 weeks ago and went to a&e, had X-Rays which we're inconclusive so I had to go back for a review and re-X-Ray 12 days later, the x rays were still inconclusive but as I still had pain they were unsure whether the wrist is actually broken so I have been advised to continue wearing the splint and wait for an MRI scan of the hand, then they will definitely be able to tell me whether it is broken or not. I still haven't been contacted with an MRI date but was told there would be a wait as it's been over Xmas time. I've had a month off work and am meant to start a new manual job in 3 weeks time but I'm worried my wrist will still be painful and not healed. If they find out my wrist has been broken all this time will I need a cast on for another 6 weeks? Or just a couple of weeks as it's been 4 already.
I'm 27 if that makes any difference