Come on Jason, not you too.
Bishop was watching the Queen hunt Newt, he wouldn't say anything if it did something suspicious? (Maybe you could argue that it's not computing properly anymore after the damage it took)
By the time we see Newt and Ripley going to their tubes, they seem recovered enough from any battle injury. Newt has survived a long time in an Alien infested area so surely she can be useful in looking out for Xeno's.
Ripley has personally seen the Queen lay an egg, you don't think she would at least try to check the immediate areas where the Queen was been (seen)?
The Queen was only in the cargo/launch bay area and it can't fly or move on the walls and ceilings so that limits the search area quite a bit. Also the eggs are not small it's not like she'd really have to check every little nook and cranny. Also the size of the Queen further limits where Eggs could've been.
And they wouldn't need months to do a search either, if you remember another rescue team would've been sent after 17 days so that opens up something questionable in the plot too why they'd go to cryo sleep unless the Sulaco didn't have supplies for that long which seems kinda strange for the amount of people sent on that mission and the few people left.
But let's follow your logic here: Ripley and Newt are unable to clear the ship because they're not capable and/or lack the resources. So they go to cryosleep where they'd be unable to respond to Alien threats (and thus be more vulnerable). Is this really how you see characters like Ripley and Newt deal with that situation?
Yeah, I can see Ripley, having just spaced ANOTHER Alien, just packing it up into cryo sleep. For starters, the Queen had a looooooooooooooooooooong egg sac thing, you can see the eggs working their way through it. So the assumption that "no egg sack = no eggs" is pretty valid. Ripley also torched all the eggs she saw and dropped a few grenades into said egg sac (pointless, BTW, since the whole site was going nuclear, but women be irrational at times) so her thinking the eggs were all destroyed was fairly reasonable. "Cryo sleep = no nightmares and wake up in safety" is also a fairly reasonable desire in that situation (plus stalling any embryo growth if Newt had been infected and just didn't know it). Plus she sees the Queen in the elevator, the Queen isn't (obviously) holding any eggs.
Obviously, had more (any, really) crew had survived then a maintenance survey of the dropship would have found the egg up in the landing well (no other place for it) but given the sequence of events Ripley witnessed, going up there to check was nowhere on anyone's priority list. Plus even if there WAS an egg (2, I suppose, one for ripley, the other for the dog unless a facehugger can implant 2) up there, if no one walked by it, the eggs seem to be dormant for years and years, who know it would hatch on its own and wander around, opening doors and shit, till it found some cryo humans and figure out how to crack their shells?
Alien 3 had to contrive a way to kill off Newt and Hicks (a TERRIBLE narrative choice, BTW) and strand an infected Ripley away from civilized space. But if you wanna re-create the Alien environment, it's what yah gotta do.