Did you warm up thoroughly? When you are new to Parkour it's often quite easy to take the amount of stress and impact even simple moves are putting on your joints, especially considering they aren't used to anything similar. I would suggest adding some joint-mobility exercises to your warm-ups, rotating your wrists, elbows, knees, etc. thoroughly before jumping into training. Also, some simple wrist stretches and strengthening exercises would help quite a bit. I may be wrong, but I think the gymnastics website http://www.drillsandskills.com has some excellent exercises that help prevent wrist injury, being that the impact from gymnastics isn't eactly a natural occurance.

Just remember, warm-up more than you would probably think would be necessary, stretch thoroughly on your off days, and take it slow, even small, simple techniques hold the potential for some extreme impact and stress on unprepared joints and muscles.

Good luck