In reply to finn rc:
Hi there, first of all sorry to hear the circumstances but well done for taking some initiative and asking the question.
As others have said you can do what you like, but a mattress isn't going to be very practical, especially if it gets wet etc. An old gym crash mat or similar with a plastic cover would be better.
I know it's hard at this stage (my climbing son is also 16) but the best thing is it find a club or a group of like-minded folk, some of whom may already own mats, and go with them.
I checked on the climbscotland website and it suggests Granite City Rock Stars - do you know them?
http://www.climbscotland.net/club-spot/club-spot-near-you/gra
You can email gcrs.chairman@gmail.com
It suggests they organise outdoor trips so that might be a good start.
They also have all the gear and the experience to show you how to use it.
Hope that helps.
Dave