I just installed a new chain on my 2002 Trek 2200 Road Bike. The old chain was a Shimano 9 speed that I installed 18 months and about 5000 miles ago. It had stretched modestly and was full of winter cruft/grime. The new chain is a SRAM 9 speed, my first time using the gold snap ring system. I followed instructions and made sure I have the same link count as the chain that came off the bike. The cassette was new with the old chain, so it has about 5000 miles on it and doesn't appear to have significant wear. After installation and a clean/wipe/lube/wipe, I took it for a 15 mile easy ride at about 15-16 mph. It shifts perfectly and I didn't have to make any adjustments to either derailleur. Three times, however, when putting it under stain (once on a modest hill climb, once starting from a stop sign in a fairly big gear, and once on an acceleration coming out of a sharp turn) it skipped several teeth and caused my foot to slam down hard. On the hill, it actually hurt as I had my weight off the saddle (not really standing) and I came down hard on the inside of my thigh. I think all three were on the right side (power train side) pedal stroke, and I don't think they were all in the same gear. I'm pretty sure it was the rear cassette that skipped, not the front chainring, but it did happen really fast each time. I will also say that it's not like these were the only three times I put substantial pressure on the pedals in the ride - I wasn't going hard, but I wasn't being tentative or anything. Also, in case it's relevant, it was cold, about 40 degrees F or about 4 degrees Centigrade.
My question: Is this going to get me hurt, or will the new chain 'settle in' over a few rides? I searched here and pretty much got confirmation of what I had previously thought, that you always get a new chain when you get a new cassette, but you should be able to get a few chains out of each cassette. Thanks!