By the time your first new knee is 6 weeks old, it should be capable of helping out your newest knee. You'll be using a walker anyway, so there won't be a problem with buckling. Don't try to move from a walker to sticks or crutches too soon. The whole point of the walker is to give you the support you need and there are no prizes for progressing too soon to a less supportive walking aid. The most important thing is not to try to do too much, too soon.
There have been people here who have both knees replaced on the same day and others who have the second knee done anything from a couple of days apart, to weeks or months apart.
Were you one of those unfortunate people who were given the impression that recovery from a PKR would be quicker than it is from a TKR? There are a few, fortunate people who have made quick recoveries, but most find that they need just as long a recovery as those who have a TKR.
I had a PKR initially and my recovery took months, not days or weeks, which was also true of my TKR recoveries.
Don't be afraid of taking the prescribed medications to relieve your pain. You've had major surgery and you need the pain relief. If you take them as prescribed, you are most unlikely to become addicted. This article may help to explain:
Myth busting: on getting addicted to pain meds
If it's at all possible, ease back on your activities. Your knee will recover better if you aren't expecting too much of it in these early days.