That would be real scary!
But I have to stress that the number one main thing to do in any panic situation like this is....don't panic! I know it's hard, but animals will pick up on your panic and panic themselves. If you are calm and talk to them in a gentle voice, it will help calm them down which will be a big help in many cases.
As an example (not a panic situation though) the first time I took Tubby and Peanut to the vet since I've lived with Terry started out as a not too good situation. Terry was so worried about the cats being in a panic in the car and at the vet, that he was all upset himself (just what I need
) Right when we're ready to go, it started pouring - and I mean buckets! He ran to the car with Peanut in the carrier, and I ran holding Tubby with his leash on. We were both soaked in the few feet it took to get to the car. Anyway, we started out and Peanut started yowling in her carrier while Tubby is all over the car exploring - I think he likes riding in the car.
So Terry, being all upset himself, and thinking Peanut is upset because of her yowling, is ranting and raving about why do they need to go to the vet anyway, they're completely healthy, and how ridiculous it was to take them out in the rain like this, and on and on. All the while, I'm talking to Peanut and trying to pet her through the bars of the carrier, but she keeps yowling and moving around. Finally I told Terry that he had to calm down and talk nice to her, that he was only making her more upset with his ranting. He was quiet for a minute, then started talking sweetly to her and almost instantly she calmed down and settled into her carrier for the trip. He looks at me with this look of total shock on his face and it was the hardest thing in the world for me to not say I told you so. 
Anyway, she could tell that her daddy was upset and that was making her more upset than the car ride was. He calmed down, she calmed down and the rest of the visit was a breeze.
So remember, don't panic. Take a deep breath, analyze the situation, then do what you can to help, even if that means leaving the cat for a minute or two to make a phone call or to get someone else to help.
PS - needless to say, I now take them to the vet by myself. The cats were fine as soon as we brought them home, but Terry was upset all day.
Tubby
Spring 1986 - Dec. 11, 2004
RIP Big Boy
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Peanut
Fall 1988 - Jan. 24, 2007
RIP Snotty Girl
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Robin
Fall 1997 - Oct. 6, 2012
RIP Sweet Monkeyhead Girl
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