Sure it gets better with time. It's still less than a month since your left TKR and complete healing of all your tissues can take as long as a year, sometimes even a little longer.
If you think about everything that was done to your knee, it's not hard to understand why it is still feeling pain. Knee replacement truly is major surgery and it does take a long time to recover. Do try not to compare your knees, because it's quite possible that your left knee had more work done than your right knee. No two knees progress exactly the same, even if they are done on the same day.
I know it's hard to be patient, but time really is your best friend. Give your knees time, don't ask too much of them now, and they should eventually be almost as good as the knees you were born with.
My right TKR is almost 5 years old and my left is almost 2 years old. Most days, I forget about them completely. I do walk completely without pain in both knees. I'm developing arthritis in my ankles and feet now and they hurt, but my knees are pain-free.
I do still feel some stiffness in both knees if I have been sitting for too long, but that soon loosens up and it has gone away by the time I walk a few steps. Occasionally, I get the odd, temporary niggle from one knee or the other, but it quickly goes away. When I think of how big those foreign bodies are that are inside my knee, I realize that I have to allow my knees a little bit of grumbling from time to time, because they are soooooooo much better than my poor old arthritic knees were.
At about a month out from surgery, you are in what we call the Dark Days of Recovery. Inside, your knee is still irritated and inflamed and it's healing as fast as it can. At this stage, your mind thinks "I should be doing so much more. What's wrong?" But your knee says "Not yet, my friend. I'm wounded, not lazy. Give me more time and I'll serve you well."
I do hope that I have been able to reassure you a bit.
United States
But for real it has been the advise here and just rest. I stopped fighting the taking a nap and reread a note that said " never stand when you can sit, never sit when you can lay down and never pass up sleeping!" I whole heartedly agree. So I begin the TRUE road to recovery now. 
I did go a little too much yesterday and paid last night. Nothing bad but just couldn't get comfy. I will fight past it with more rest today but still somewhat active. I find some days I think I sit to much and that starts my issues. Once I pass that I am good. @uva55 Clara. I have wondered about you and work. How's it going ? Hope good. I wish you well my friend and continue to heal with you.
. I did finally get pain down to a manageable state. I will sleep ok tonight I can feel that. Another shower time tonight and that was 
. I hope this weather straightens out soon to. That might help. I walked to mailbox today as well. I like to get things done but must remember " your not 25 "
