While I understand your doctor's sentiments, I suggest you get a second opinion. There are active people who have more than one knee replacement during a lifetime. IF surgery would fix your knees, it may be worth having a second knee replacement later in life. You'll probably need to curtail some of your activity, but your existing injury may require that anyway!
The brain tells the body to make subtle changes in how we stand, run, walk, and anything else that may impact your arthritic knees. This compensation causes subtle changes that may create problems in other joints.
Exercise gently while you research non-medical treatments. Since osteoarthritis is a wear and tear disorder, exercise may speed deterioration of your cartilage. You haven't said how your doctor discovered your osteoarthritis. Did he order xrays? Did your knee swell after your injury? Is the knee still painful?
Pain that does not ease after 6 weeks should be investigated, closely, so that it does not become chronic, intractable pain.