SuperEgg, you've gone a long way toward answering your own question. And, nice detective work too!
There are two ways to deal with anxiety (and anxiety attacks).
The first is to know as much as you can about what triggers them, so you can predict when they may come and under what circumstances.
The second is to know what to do if a panic attack or big time anxiety does occur.
Lots of times when we're learning about ourselves and our anxiety we have to look back to see what happened- and this is exactly what you did (total Gold star :)
You realized that you were feeling pressure to have your daughter's school project be perfect, and that this was causing you great anxiety.
So... the next time she has a school project (which we know she will, right, because school is filled with projects) you will be able to predict that this "OMG, it has to be perfect" thing will come up for you (there's NO shame in it coming up for you, by the way, the only thing that's important is that you notice and then make decisions about if you want to act on it- which you told us you do not, since you don't want your daughter to have to try to be perfect).
If/When it arises you can say to yourself, "oh yeah, I totally expected you... no surprise at all....I totally predicted you'd speak up here..."
This should really help with the anxiety- because one of the big things that triggers huge anxiety and panic attacks is Surprise and Unpredictability and feelings of Chaos that we can't control. You'll be able to reassure yourself that you saw this coming, that you've experienced it before, that you know what it is, and that it won't harm you.
If you still do get overwhelming anxiety, it's ok. This may take a little practice so don't worry if you still feel panicky the next time you're working on a project- you really will get good at this, and used to it.
If you do become panicky, put the scissors down (seriously), uncross your legs or stand up and walk around a bit- fresh air is often a good thing. Work on breathing (anxiety makes us breath very shallowly and this does not help anxiety at all- in fact, it makes it worse!). Try to talk to yourself as you would to your daughter if she was frightened (in that cool, calm, collected, gentle voice I'm sure you use with her). Also, remind yourself that you are panicking because of things that have to do with your own experience being a kid- not because of anything that's running amok in the present. This is important because when we panic we sometimes have trouble distinguishing between he present and the past. Remind yourself that your daughter is fine, and that you are fine also (because you are).
This combination of preparing/predicting anxiety and having a plan for what to do if it does come is the most powerful and effective way of dealing with big anxiety.
Try it out, make adjustments that work for you, and of course, ask questions (like you did by asking this one on the blog) so you can get the answers you want and need.