M75.110 Incomplete rotator cuff tear or rupture of unspecified shoulder, not specified as traumatic. M75.111 Incomplete rotator cuff tear or rupture of right shoulder, not specified as traumatic.
Within that window of time, your eggs will be at their highest quality, meaning the yolk will be high and upstanding, and the white will be tall and firm when you whip them. According to Foodsafety.gov, raw eggs in the shell can be kept in the refrigerator for three to five weeks. Freezing in the shell is not recommended. Instead, crack those eggs, beat them, and then store them in a freezer-safe container. More: 10 smart ways to use up leftover egg yolks.
Lastly, you can do what you are already doing, and store them with some towels, but they will probably express some water. The eggs should be good for about one week, unpeeled. The Egg Board recommends they be eaten the same day they are peeled, but other sources indicate up to about 5 days.