There are a lot of answers giving you information, but I don;t think anyone has mentioned my symptoms.
Last November my left leg became swollen, whilst my other leg was normal. It wasn't painful and as I have quite a few 'old age' conditions, I just assumed that it would go down again. However, 3 days later, my next door neighbour asked me to go and witness a document for her, and I took about 7 steps to the end of my drive and had to stop to get my breath back; I then took another 7 steps to her front door and had to clutch at the wall whilst I recovered again.
When I returned home I googled and found a comment that if you had just one swollen limb it could be to do with blood clotting.
To cut the story short, I phoned the surgery and mentioned what I'd read, and got an appointment that afternoon. GP examined me, consulted with Senior partner and then sent me to A&E with a note, but also phoned them to say I was coming.
I expected a long wait - could see there were a lot of people in the Waiting room, but I was put in a wheelchair and taken straight through to RESUS.
Spent the next 3 weeks in hospital wearing an oxygen mask the whole time, apart from when eating. Was put on blood thinners ( Apixaban) immediately when discharged and have just had the dosage reduced after 6 months.
It may well be because of my age ( nearly an octogenarian that whilst I was there I had all sorts of tests - there was no 'nursing' but loads of computer driven tests - to the extent of sometimes waking me up in the middle of the night to do a blood test - had 3 cannulas attached to each arm!
I won't bore you with the aftermath except to say it took me a long time to recover, but I thought it might be useful to be aware that a swollen limb could be warning signal.