I think you hit the nail on the head. Sounds like a panic attack to me. Your daughter is probably hyperventilating when she crys, which leads her to feeling like she can't breathe. Point out to her that she is breathing just find or she wouldn't be talking. I agree getting her to lie down in this panic state would be difficult. Try to divert her attention from her breathing. The more she concentrates on it the worse it will get.
When we inhale, air enters our lungs. In the lungs, oxygen crosses into the blood stream and carbon dioxide crosses out of the blood stream. The carbon dioxide is then exhaled out. We always have a combination of these two gases in our bodies. When someone gets overexcited, respiratory rate goes up and we exhale more carbon dioxide. Sometimes we exhale too much carbon dioxide.
Carbon dioxide helps to balance the Ph of our bodies. The normal Ph of the human body is between 7.35 and 7.45. Carbon dioxide = acid. Too much carbon dioxide (Co2) and the Ph drops below 7.35 and the body becomes acidic. Too little Co2, and the Ph raises above 7.45 and the body becomes alkalotic.
I know this sounds more complicated then it needs to, but it helps to understand that the symptoms are real. When your daughter exhales too much Co2 and becomes alkalotic this can increase her anxious feelings. Of course, these anxious feelings will cause her to struggle even more to breath which of course increases the amount of Co2 she is exhaling and worsening the problem. Ultimately, this will not harm her and her breathing will regulate, but it is quite uncomfortable.
Redirecting her in a physical manner, not only is distracting, but doing something active increases her body's need for oxygen, therefore, requiring a higher respiratory rate and in essence you increase the need for oxygen to meet her higher respiratory rate and the body's Ph becomes balanced.
Many people also will breath into a paper bag which will assist them in rebreathing their own exhaled Co2 and in that way balancing Ph. I just think it is difficult to get a 6 year old to breath into a paper bag.
Of course, if the problem persists, or your gut tells you there is something more involved, then speak to your pediatrician, although unlikely, there is the remote possiblily that your daughter has some other physical cause for these symptoms.