Running and pooping all over the house and panting at the same time is very unusual. It doesn't sound like a constipation problem, since she's pooping a couple of times a day. Was she very constipated at one time and passed a large stool that caused an anal fissure? So, every time she poops now it hurts her...that might account for the anticipation of pain and the panting. Panting is a pain or extreme stress reaction. Whatever it is, she has certainly got herself in a state about defecating, and it's triggered her "fight or flight" reaction---flight in her case!
Perhaps a mild sedative from the vet might get her anxiety calmed down, or homeopathic "Rescue Remedy". If you've only got one litter box, a second is recommended in a different, quiet location.
Keep us posted, this is unusual behaviour.
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