Yep....this is way too much for you right now and your body's is telling you that with the pain and restless legs you're experiencing. And not enough icing. Applying ice for 15-30 minutes doesn't really do anything for pain. You need to ice at least 45 minutes (more is better) and you can actually keep ice on your knee as much as you want as long as you use a kitchen towel to keep the cold away from your skin. Your gel pack may feel "cool" midway through the night, but it's not enough for TKR recovery. You need to swap out the gel pack at least once during the night. I had 4 that I used for both knees. I would use two at a time so I could ice all around the knee, and then would switch them midway through the night. You need to ice the back of your knee because swelling can occur there.
I recommend that you scale your activity and exercises way back for a couple of weeks and see how things go. Continue with your pain medication on a schedule and frequent icing during this period. You don't need a lot of fancy exercises right now for your knee to improve. Your goal is to get the inflammation and swelling down. Even if you don't see swelling, it is there. The knee capsule is very compact and it doesn't take much fluid to cause pain and reduced movement. I don't know what exercises you have been doing, but switch to just some gentle bends and stretches for about 5 minutes (working up to 10 minutes) every couple of hours. If you want to walk a bit, that's okay, but start with 10 minutes and make that one of your "movement" periods. If you have an exercise bike, you can also do rotations on it as one of your bend/stretch times, but only for 5 minutes. Keep this up for two weeks and see if things settle down a bit. Your knee is probably very inflamed and angry right now and it does take a while for that to calm down.
Stairs are quite taxing on a new knee, so you need to keep those trips at a minimum. How about making your bed and attending to the litter box when you first get up before going downstairs for breakfast? Then, when you get downstairs, lie down and put your knee up with ice for 45 minutes before getting up to do breakfast. The idea is just to do one short task or exercise every hour or two and then rest/ice/elevate for at least 45 minutes.
If you're not using a cane or walker, you need to be. Use whichever aid allows you to walk with no limp. Don't worry about trying to go down the steps normally. You can even go up and down sideways holding on to the rail so as not to stress your knee soft tissues.
Also watch how much time you spend sitting upright with your feet on the floor. That can really increase swelling as well because of gravity. Your "resting" periods should be lying down, with ice, and your leg elevated so that toes are above your nose.
If you will give this a try for at least two weeks, I believe you'll see some improvement in your pain levels. The next time you speak to your surgeon or your GP, you could ask for a prescription for Tramadol. It can be used very effectively with Tylenol for those times when you are having trouble sleeping at night or your pain levels are elevated. Tramadol is a "step down" pain prescription and not considered an opioid, so it's usually something most doctors will agree to if you are still in pain.