There is no clear answer and a great deal of differences of opinion. One of the problems is that depending on the person and the compression stoicking they vary greatly in the "tightness". Too much tightness impedes circulation, and when you wear them continually, this is not so good.
The swelling is from lymphatic fluid.
If the compression stocking are not too tight, Generally the doctor will check on this by having you wear the stockings for ten minutes and then checking the dorsalis pedis pulse, on the right foot and the left foot. There should be a strong pulse. If so there is no harm in wearing them every day. At night they should be removed and your legs elevated.
When you take them off, if you have one on each leg, you should wait a few minutes before taking off the second stocking. The reason is that the blood PH is altered slightly when they are worn in the area below the stocking, Taking off a stocking changes the PH of the blood, just as when then MAST trousers are removed. If you take a few minutes after taking off one stocking, the blood will become normal again, generally because of a slight alteration in the breathing rate, thus diminishing the chances of PVC's which occur when the blood PH is rapidly altered.
Cutting to the chase - Is it significant to wait a few minutes before taking off the second stocking after both have been worn for a few hours? Probably, not, but it is good practice to do so.
Did your doctor prescribe your compression socks?