Ovinomancer
No flips for you!
This boils down to "just improv." That's not an easy ask -- you have performance anxiety involved and you have people that just don't quickly think on their feet like this. Sure, you can learn it, but it's not useful advice earlier on without a lot more concrete outcomes. Fundamentally, using improv successfully in D&D with requires a strong confidence on when to complete ignore the rules and wing it or a much more fundamental change to how you run the game.
My suggestions for prepping your own material are to keep things tightly constrained -- this prevents you from locking down with option paralysis or feeling like you need to connect everything. You really don't. Look up the 5-room dungeon design. This is an excellent way to format a lot of adventure content -- not just dungeons! You basically draw 5 circles and then connect them with lines -- usually using only one or two branches. Then, you pick a few of the the "room" types from the list and you've now got an outline of both what should be in each "room" and how those "rooms" connect. I keep quoting "room" because it doesn't have to be a room -- you can make them social events in a courtly intrigue plot, or wilderness locations during an exploration or travel segment, or, you know, actual rooms in a dungeon. The framework is very flexible and provides a strong core to design around.
Then, if you're having trouble with more content, stay classic -- use an encounter generator like Kobold Fight Club to create a random encounter, and if it speaks to you, use that monster combo to build out your adventure. This is a good way to pull from appropriate enemies without reading over all of the books. KFC is also great for planning and balancing encounters. If you're players are steamrolling encounters you've set up, just up their level by 1 or 2 in the tool and present those encounters.
Details are a trick, though -- providing details is something that makes a scene memorable and can be hard to come up with. I'd suggest coming up with a theme for your area and then threading that through. Remember to add a detail for each sense -- not all at once or all the time, but sprinkled here and there. Foul smells, walls that are damp to the touch, cold drafts, dripping water, distant snarling -- all of these both help bring the scene alive and give you the ability to foreshadow.
Finally, don't prep outcomes. This is where a lot of GMs get into trouble -- they're assuming a specific outcome from a scene and, if the players fail or they do something else, the prep fails the GM and they have to scramble to adjust. Some GMs do this naturally, some learn. You can avoid this entirely if you don't assume outcomes and instead just focus on preparing locations. If you use the 5 room dungeon, pick a theme, and set up your encounters (remember to do a little thinking on what the creatures in a given encounter want), then you have a strong framework that you can lean if the players surprise you. Since you don't have a required outcome for the adventure, they players can't fail to achieve it and leave you stumped. If they players do something you didn't anticipate, that's fine, because you didn't really anticipate them doing anything specific and you can look to your prep to form an answer. If they ask you a question you didn't think of before, again, you have a good prep -- look at your theme and your rooms and encounters and you can usually find an easy answers.
On a different note, don't be afraid to say you need a minute to think -- your players will forgive you (if they don't, you need to not game with jerks -- no gaming is better than bad gaming). Also, don't be afraid to ask your players to help you out with some things -- if they've asked you a question and you're stumped, turn it around and ask them what they think the answer is. If you like what they say, go with it, "yup, sounds good, let's go with that." I'd also strongly recommend that you do not let players either make rolls on their own or ask to make rolls. This puts you in a position of accepting a roll where you didn't already think through what happens on a success and what happens on a failure and makes you have to improvise without good inputs. If a player asks to make a roll, ask what their doing and what they want out of it -- this gives you the needed inputs to decide if a roll is even necessary and, if it is, what the stakes and actions are. This will help a good deal with feeling like you have to have an answer for everything -- don't let them ask you questions that don't have plenty of player input into what's going on. "I rolled a 20 perception, what do I see," is a terrible question -- you may feel like a high roll deserves something you didn't prep, and now your ad-libbing. Instead, err on the side of sharing all the important details in your scene description so the answer to this question is 'the same things I already told you about, unless you're doing something specific?" This puts more work on the players to engage the game and takes some work off your shoulders. Of course, as with any advice, there's likely exceptions or preferences where you're comfortable with some asks for rolls and don't mind them. If so, go with it. Personally, I don't allow any asks for rolls, just action declarations where I ask for rolls if I think they're uncertain.
