Hi,
I'm sorry to hear that Lucy is having these issue. The pulling of the fur on the tail can indicate several things. Some of the main culprits are allergies (this can range from food to fleas to applied products) and thyroid disorders. The later is of interest in that heart conditions sometimes run in tandem with this. This may account for the coughing and vomitting following her runs. Additionally, some adrenal issues can also cause both of these symptoms. It would be advisable to have her into your vet for a "wellness" exam to get this pinpointed. I hope she's doing better soon.
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