The OTC Aleve is naproxen. My doc recommended it for my tendonitis (elbow) but I was not thrilled with the results and went back to ibuprofen (Advil).
Ok, I have a bad knee but its from osteoarthritis, and I have tendonitis, but not in my knee. So I guess I’m half qualified X 2 to answer your question. 
re: tendonitis. Have you tried a compression sleeve for your knee? I have this thingy for my elbow, it’s just a tube of woven fabric that’s stretchy, that I wear over my elbow. It’s about 8 or 10 inches long, and machine washable. I tried to get my PT to explain why it made my arm feel so frickin’ much better, but I got a little lost. Basically, what I gleaned is that it keeps inflammation out of the area and at the same time gently massages it. I’m not sure where you can get a piece of this material other than at a physical therapist’s, but you might give support hose a try just by way of experiment. A pull-on brace that covers most of your knee might have a similar effect.
re: icing: highly recommended for both my knee when I overdo it and elbow tendonitis. There are two methods: passive icing and ice massage.
*You know what passive icing is: you hold the cold thing to the thing that hurts. 10 minutes on, take it off for 10 minutes, and then back on for another 10 (total elapsed time: 30 minutes. total icing time: 20 minutes). BTW, you can make a cheap reusable “slush pack” by mixing 1/2 cup rubbing alchohol with 1 cup water in a ziploc, and freezing it. As you may know, never passive ice against bare skin – always have a cloth barrier to prevent frostbite.
*In ice massage, you actively rub the place that hurts with bare ice (water frozen in a dixie cup is generally recommended). You move the ice constantly, rubbing in a generally circular manner around the affected area, and you do it for about 5-7 minutes. Keep peeling back the dixie cup as the ice melts. As you ice massage it should go from “feeling cold” to “deep aching” to “totally numb.” Let me reiterate, never stop moving the ice, or, once again, frostbite. (no cloth barrier with ice massage).
The benefits of both types of icing last about 4-6 hours per application, so 3 times per day is ideal. I used to do ice massage at work (quicker) and passive when I got home (lazier). And the sooner after strain you ice, the better off you are. So, for example, ice immediately after practice or the minute you get home.