Recently Diagnosed with an arthritic hip

I’m 71 and recently diagnosed with an arthritic right hip. Previously ( 6 months ago) very active ..walking, badminton, swimming, yoga so this is life changing for me and will take a while to adjust. 

 The consultant says exercise will not make it worse so I’m still walking although not so far or fast and obviously not enjoying it so much, and practicing yoga with adjustments for the impingement. I can’t play badminton anymore but will resume swimming soon. 

I’m keen to find out if I should be doing other strengthening exercises to maintain maximum mobility for as long as possible. 

I’ve also been told not to be afraid to use painkillers..I find one paracetamol and one ibuprofen sees me through a day, but am reluctant to take them every day…what do others do?

 I’d be grateful for any suggestions or to hear from people with a similar outlook.