My boss has the same as you and was on growth hormones but I think from about age 11. She is 5'3" so may have benefitted from her condition being discovered earlier.
What does your doctor believe will happen if you take medicine for growth? Is there a negative side to it that is preventing him from prescribing? That's what I'd be asking.
And, given that time is of the essence, would be be prepared to do another x-ray? Or, could you get a second opinion.
I think it depends - some people continue growth in early 20's. However my son's friend had a condition where his legs had stopped growing as the platelets had already bonded when he was 17. So it's obviously dependant on the individual. Good luck.
There is an 'experts' forum here where your poste would be answered by a doctor is no-one else chimes in. There are a few with your condition, but it's a more rare thyroid condition.
http://www.medhelp.org/forums/Thyroid-Disease--Hypothyroidism/show/1261
I also searched 'growth hormone' in this site and came up with a number of posts in different forums, one that recommended another site: http://health.groups.yahoo.com/group/thehypopituitaryalliance
Go for gold and get all the answers from wherever you can until you're satisfied in yourself, and/or found something that you can take to your doctor.