I'm a physio- pm me if you want advice.
Physio rather than a chiropractor would be better in this instance.
Where do you live? certainly you can go via your GP for NHS referral, the differences between NHS and private are nil with regards to training, so don't think that because it is a private physio, they are better, that said, the waiting list for NHS physio may be huge, so if it's something that can't wait then private is the way to go.
Private will most likely try treatments to keep you on as long as possible, whereas NHS are conscious of wating lists and want you out the door asap (although with both, this is not always the case)
Private will cost you about £40, but you will get a longer treatment session, NHS is obviously free, but most likely within work hours for a shorter time.
NHS waiting times vary depending on the clinic, and some place you can self refer into without going via gp.
it is always a good idea to pop a referal in, and if you need private physio during the wait even for a one off session, at least you've started the ball rolling.
The crossed leg part could be a meniscal or ligament injury, and the sitting for a long period could mean patellofemoral pain, all of which would need a proper assessment, but certainly specific quads strengthening exercises would probably be the way to go.
As i said, pm me and i can give some advice.
m xx