At the risk of decreasing the tempo, a solution to this may be consistently keeping players in check.
It’s easy for a group of players to get excited, due to the nature of play. More often than not, players will begin talking louder and louder without realizing, simply because the overall noise level of the table has grown (from talking).
For this situation, you can treat the players a lot like you would treat a classroom. Distinctly and specifically call for responses when you’re looking for them, encourage people not to interrupt, and remain consistent with your statements/
If the players are beginning to raise above the din of normal speech, take the authority of calmly reminding them to settle down a little. To ensure that this doesn’t come off as accusatory, keep a calm demeanor and be consistent on your checks.
Alternatively, try playing games that encourage a more laid-back atmosphere rather than an active or frenetic style of play. “Slice of Life” games are rarer, but do exist in the tabletop scene.
I hope this helps. If anyone else has advice, please feel free to drop it in!
I know this is like, five days old, but as a notoriously anxious DM I felt the need to comment.
Communication is important. Remind players if they get loud to quiet down. If you’re feeling overwhelmed by the amount of noise and verbal input, speak up. Often a “Hey guys, one at a time” works well enough. Get everyone quiet. Then point to someone you know was talking, let them say what they were going to say, and move on to the next person, one at a time.
This one-at-a-time thing cuts down on noise, makes it easier for you to get information from the situation, and allows everyone a chance to speak. That last one can be really important if your noise level has escalated and one of your quieter players has been drowned out. DMs have a lot on their plates, and in my experience players have not gotten upset when I insist on dropping into conversational bullet time to sort out what everyone’s saying.
If you find it too overwhelming to talk during these situations, try getting a bell or other alternate sound device that can get people’s attention and prompt them to quiet down. (I have not managed to train my players to do this, but it may be worth a shot in your case.)
Like CP said, it can be like managing a classroom, so do your best to stay calm and reel in the social situation. This is a fun event, so there’s no need to be a strict disciplinarian, but be assertive: you hold the title of Dungeon Master and people will listen to you without you needing to be a tyrant. Unlike a classroom, though, you are not a teacher, you are a mediator and a peer. All players, DMs included, need to make sure to communicate with the table when conditions don’t allow for everyone to do their jobs well, whether it is participating in the game or running it.
good luck! and don’t forget this very important post from CP if you are ever feeling anxious about other parts of running a game.