Have pain in the back of my knee, no swelling redness or warmth, haven't injured it; could it a blood clot or dvt?
Could be a cyst. You can get an ultrasound to look for "bakers cyst".
Not likely. Pain may be dvt, but, is more likely soft tissue inflammation or a cyst behind the knee. An ultrasound can painlessly and easily rule out DVT and help sort this out.
DVT possible but... While it is impossible to exclude DVT as a diagnosis, more likely you have a benign baker's cyst. These are common fluid connections in the back of the knee joint. They may be a bit painful and sometimes the cyst can burst, causing swelling and more acute pain. An ultrasound at an urgent care or through yor doctor can confirm either diagnosis.
Maybe. If there is no injury it could be a muscle, ligament, tendon injury or bakers cyst. Blood clots are possible and would not need to be red swollen or painful. Best advice is get examined please.