Hello, Thank you for asking your query at DoctorSpring.
Your symptoms of lump at back of knee and upper thigh swelling and burning feeling points out to one diagnosis: Baker's cyst.
Baker's cyst is a lump behind the knee, basically a poket filled with synovial fluid. It could have happened after a trauma, a knee injury. At times, the fluid in the pocket can leak out into tissues of lower leg causing swelling and redness in that part of the leg.
A Baker's cyst usually is self-limited and goes away on its own. Here are some conservative measures you can do at home to relieve your pain. You can take over the counter pain killers like ibuprofen and naproxen. I suggest your leg as much as you can. You can use a crunch or walker to give your knee rest. If you still have these symptoms after 2 weeks or if there is another problem arising I suggest you visit a surgeon. The surgeon will look in if there is too much of fluid accumulation, in such a case he will have to drain it out.
Hope this helps. Please feel free to ask follow-up questions.