Robbing is a problem for small hives/nucs (and even big ones, too, when there's a serious dearth of nectar), but there's no reason to believe that your queen is dead simply from the robbing. The robbers aren't there to take over the hive (except if you live in an area with Africanized Honey bees which have been known to try to usurp a hive). The robbers just want to steal the honey away.
But robbing, aside from losing desperately needed supplies, also exposes your bees to parasites and diseases brought in by the robbers so you must get it stopped.
The huge crowds of bees outside and around the robbing screen may also just be some of your own bees confused about the new entrance procedures. It's pretty common, even without robbing pressures for a robbing screen to bewilder some of your bees, at first. This will abate in a day or so. You can go out in the dark and take the robbing screen off to let your own bees back inside for the night. The robbers will have gone home by then.
Then put some re-orientation barriers up in the a.m. before dawn so your bees have to think about their approach and departure paths a bit. You may see some of your own bees doing that re-orientation circling in front of the hive. This is good thing and it will make them more efficient about navigating the robbing screen.
Which brings up a question: do you know how to differentiate between a big crowd of orienting bees and a true robbing melee? I ask because the first time I saw a significant bunch of orienting bees I was sure my hives were under attack from a battalion of robbers. The key thing is that orienting happens in middle and late part of the afternoon and lasts only 30 to 45 minutes and then poof, it's gone back inside the hive. Robbing starts early and ends only at dark. Plus the demeanor of the bees is different.
You can run with both a robbing screen and a little block of wood in the entrance so there are two barriers. I did that when my bees were under assault last summer.
Make sure you are not open feeding (or using a Boardman-type feeder attached to the outside of the hive) or having any honey around in the open.
You can open the hives to check on them but try to keep things pretty buttoned while doing so; meaning don't lean a side frame against the hive to make room to remove the others. Any frame that's out of the hive should be temporarily installed in an empty hive body with screened bottom entrance and a closed top. If temps allow, I'd do any insection as early in the morning as possible and hope the robbers were sleeeping in a bit.
I'd also plan on checking your varroa levels soon as the robbers may have brought them in if you didn't have them before. And double check the pictures and descriptions of hive diseases and watch for them on the combs, too.
If you are running with a screened bottom board only, I'd consider some kind of partial, or secondary solid layer below it. I found it made my bees crazy having robbers banging on the screened floor below the hive all day long, even when they couldn't get in. Just preventing that calmed my house bees down considerably and allowed them to focus on the actual assault points.
If it's hot where you are and you need to reduce your entrances a good deal, consider adding some secondary, double screened (bee-proof screening on both sides of box walls) ventilation points. And be sure to use true bee-proof screening, as robbers will take advantage of looser meshes.
It's a good suggestion to consider moving your hive, if that's an option.
The other thing to remember is that I've found that robbing makes your own bees much more cranky than usual so be sure to take extra precautions about suiting up, even if you normally work them without a jacket or gloves. A little spritz of Honey B Healthy in water will make them a bit calmer, but make no mistake, the bees know they are under mortal attack so they are extra vigilant. (And bees being bees, they'd return the favor at any hive that they found insufficiently protected. Yes, that goes for your Sweet L'il Darlings, too!)
Good luck!
Enj.