I have recently started playing rugby and during and after my ankles and wrists hurt, I also get back ache. Osteoporosis also runs in the family?

Sounds like you. Just started playing rugby and may not have been quite in enough physical shape but it is unlikely related to any osteoporosis issue as that condition is painless until a fracture occurs due to the decreased bone density.
Not Osteoporosis. I do not believe osteoporosis would affect somebody like you active in good physical shape even he have family history of osteoporosis. Most likely you need some stretching exercise before the games and strengthen exercises. Good luck.