Could be several things. One might depend on the technique she's using when swimming. Probably the force of the water when she strokes thru it, is straining the joints that go to her hands and feet. She can fix this one of two ways. If she's just letting her hands and feet flop thru the water, she should cup her hands and roll her toes downward when she strokes and kicks. But if she's already doing that, then she is doing it too strongly and it's tiring out her joints, so she shouldn't resist the water so strongly and relax her hands and feet a little more. And could be a little strength training of the arms and legs will help her in either case.
There's also a possibility that the water she's swimming in is so cold that, since the extremeties are the first to lose heat, the sensation she's got is from the cold... extra body weight can increase this circulation thing. If the pool is indeed cold, then she shouldn't have to swim in it so long or somebody needs to address how awful that pool water is. Then there's the idea that the movement of swimming is twisting her back, to where the nerves are complaining, and to change that I suppose she could do exercises away from the pool that will tighten the muscles that support the spine, which include the tummy muscles, and the back and shoulder muscles.
But if despite all this and her joints still bother her, then you may wish to consult with a rheumatologist and get to the bottom of this joint problem, she may have some form of arthritis that is doing this to her. And then there's a possibility that the nerves that go thru her wrists and ankles aren't working right when stressed, kind of like carpal tunnel syndrome, and thus a neurologist might be your next step, because could be it's simply the way she's built. He could also check out how her spine is doing, in case the twisting motion of swimming is bothering it more than the average person, on account of some other physiological problem.
Thank you. Actually, she is a thin girl, and she has scoliosis, about 8% curviture, and she has Reynauds, where her fingers & toes go white, numb, then blue when it's cold. She hadn't complained about that with swimming, but I bet it has something to do with it. I'll have her read your reply, thank you for your help!