How long does it take to heal a fractured elbow?

About 2 months ago, i was riding a bike and fell and landed on outstretched arms. I couldnt move my arm at all the first day. so i go get xrays. the doctor at first looks at it and says nothing is wrong maybe just strained muscles. but i get a call later and he found a nondislocated fracture of my radial head. i let it rest for about a month in a sling with limited movement. now, 2 months later, i have no pain at all but i cant completely outstretch it. when i say no pain i mean i cant even notice i fractured it. but i just got back into exercising (minor weightlifting and pushups and swimming) and i went back to work washing dishes (**** job :) ) but i woke up this morning and now its sore.....i was wondering how long it would take to heal?