It's something that you need if you're not a member of a running club, and it's standard in a number of countries (certainly ones with a French influence). You can download one from the Paris Marathon website, http://www.parismarathon.com/marathon/2009/docs/CertificatM_GB.pdf
It needs to be less than 12 months old, but within that time you can re-use it for different events (I'd chop off the race-specific information on the Paris one). The basic point is that if you drop dead,the race organisers are covered.
May be worth getting even if you are a member of a running club, just to be on the safe side! My doctor charges for this, but not all do.
You'll need to take your passport along to get your number as well.
The physio's idea was that both the shoulder pain when running and the hunching (which affects me more when I'm on a computer - like now!) were due to a weakness in the muscles under the shoulder blade, most likely in the trapezius muscle. Some of the exercises I was given are on <http://www.ohsu.edu/academic/som/orthopaedics/dc_cuff.htm>. There were also a number of stretches. The idea was that this weakness led to poor posture, which really told in situations of strain.
I do seem to have had these pains less frequently since doing these exercises. Though to be honest, I haven't run myself to the point of tiredness much recently!
Having said all that, the physio didn't seem to have encountered the condition before. And I've never met anyone else who suffers from it. So if you do find anything helpful out, I'd be interested to know!
It sounds like something I've had, on and off, for years. I find it mainly occurs when I'm going downhill. Like you I find that bringing the arm in front of the body helps - sometimes I rest it on the waist-bag I carry, or just dangle it like a weight, for a bit.
I consulted a physio, who diagnosed weakness in the muscles under the shoulder blades, and a series of stretches and exercises. They seem to have helped a bit. But if you find out anything more definite, I'd be interested to know! The physio seemed to think it was connected to my tendency to hunch my shoulders when concentrating, leading to face ache, tension headaches and migraines. Can't say these have improved much.