Some of my pigs, particularly when they were younger, were hard to catch, and would totally rip up my arm with their nails. Hadley on top of it used to shriek if she was feeling particularly feisty! Being picked up is stressful for guinea pigs, it cuts very close to their natural instincts as a prey animal. In the wild, nothing picks you up to cuddle you! So it's natural for them to instinctively fear this experience. Guinea pigs who feel threatened tend to either freeze or run- she's evidently gone through the freezing period (which actually indicates greater fear in a lot of cases) and is into running. You can try to make it easier for her by picking her up in a fleece, or a tube or something like that, but ultimately if you've got to pick her up for medical care, you've got to pick her up for medical care and will just have to catch her. I agree with giving her a treat and such as positive reinforcement when you do pick her up. I did find that my pigs mellowed out with age and catching them was no longer a big deal (though some of mine are more opinionated about when they get picked up... Hadley in particular is happy to be picked up most of the time but is also really stubborn, so if there is something she wants to do instead she will kick up a fuss.)
