Most unaffiliated classes won't have an age limit on them, so you'll be able to do them.
At affiliated level you'll be in the 13hh-14hh category - most affiliated classes will have an age limit - the BSPS (which is the association for most of the whp classes at major shows) says that for this height category "riders must not have attained their 17th birthday before the 1st of January in the current year", so yes, unfortunately you would be too old. The NPS have some classes with no age limit, but I haven't seen many of their shows around. I believe PUK has the same age category as BSPS, but it's worth checking their website/rulebook.