I am still having trouble lifting my leg though I can walk with the aid of the walker but my knee really hurts a lot and there is still a lot of swelling which impedes my bending for physiotherapy. I feel I am really lagging behind in my recovery
It's only 10 days since you had this major surgery and you are not lagging behind at all.
Recovery from a knee replacement can take as long as a full year, although you will be able to do most things by about 3 months.
There is no time line by which you have to achieve certain milestones of achieve good Range of Motion (ROM). You have plenty of time, because ROM can continue to improve for a year, or even longer, after surgery.
Myth busting: the "window of opportunity" in TKR
Of course your knee is still swollen - it's been through major surgery and it needs time and gentle treatment, so it can start to heal.
Swelling takes a long time to go down completely, but you an help it by doing lots of rest, elevation and icing.
There are articles about elevation and icing in the recovery guidelines, which I will post for you in my next message.
Don't let anyone tell you that you are behind, because you're not. Your knee will recover on its own agenda, not some artificial timeline set by your physiotherapist.
In any case, it's not exercising that gets you your ROM - it's time. Time to recover, time for swelling and pain to settle, and time to heal. Your knee has the potential to achieve good ROM right from the start, but it's prevented from doing so by swelling and pain. As it heals and the swelling goes down, your ROM (both flexion and extension) will increase spontaneously, whether you do formal PT (physiotherapy) or just let your normal Activities of Daily Living (ADLs) be your exercise.