First time poster, be gentle

I am a government employee who is traveling internationally later this week for official travel. I am 6'5" tall and have recently torn the meniscus in my knee. I would have had surgery done at this point but they didn't want to operate so close to airline travel for fear of blood clot. So, I have to wait until after I get back.

My question is this... what should I do to get a better seat? Being tall, I normally have enough trouble flying as it is but I am especially worried about my injured knee. I don't have elite status, and I only have about 6000 frequent flier miles. I am flying United Airlines on an S class ticket, bought through government travel agent.

Would a polite sob story help me any? Arriving early? Arriving late? Doctor's note? Any tips? What do I do?

Thanks!