LOL... you brought back some memories with this about days with my son! Thankfully I have not had to deal with them YET with my daughter!
When my son would do this I would get really close to him and blow hard in his face- more towards his mouth and nose. This usually would get him to take a huge breath and all would be good. If that failed- I gave him a little pinch (the fatty part under the arm).... sounds cruel but it worked and I was petrified and willing to try anything. The shock would cause him to gasp.
I do like the previous posters idea of water. I will use that as my last resort if I have to go through this with my daughter!
I have caused myself to pass out in the past from pain. I would be holding my breath... I do not realize it! But my hubby would be yelling at me to breathe- poor guy. As soon as I started to go down I would gasp he says and then in midfall I would come to. Makes no sense to me! Guess the brain knows what it is doing!!!
If she passes out she will start to breath again on her own- typically... if not of course call 911 and do what is necessary. Once she is down though on the floor raise her feet (brings blood back to her core and brain) and just talk calmly to her. She will be just as scared as you are when she comes to!
Also, not sure how your daughter is... I have been doing deep breathing with mine in the very beginning of a tantrum. I will whisper while she is screaming and tell her to take some deep breaths. I have her close her eyes and just listen. Sometimes it works sometimes it doesnt! She does not understand time-out still so that does not work! I also sometimes will have her do some yoga she learned from Sprout on tv.... works for her and maybe it will for you also! And of course there are consequences for the behaviours she was showing in the end... I never just let it slide! But atleast she is calm enough to work with me! (i will admit this is new to me- I am old school and decided to give this a try and so far not bad!)
I really wish you lots of luck! Biggest thing to remember is to keep your calm about you no matter what happens! Blessings to you and yours!