Hi. So a feeling like your heart is skipping a beat is called a palpitation. It's important to note that most of the time, it isn't anything to worry about! But if you have any other symptoms with it like shortness of breath, heavy sweating or dizziness, that's considered an emergency and time to get checked out immediately as those are signs of a heart attack.
You mention your period. Hormones WILL affect your heart and can cause this. So, ya. Your cycle and/ or period can cause this. Stress can as well and I always have that around the time of my period too. Like I just don't cope as well. Sigh. (plus I'm a mom which I swear adds to it).
I think since you also mention that you have the breath issue and this happens periodically and not just isolated incidents, I'd tell your doctor and see if they want to follow up with any tests. It's likely hormonally related since you've tracked it. Here's information https://www.webmd.com/heart-disease/atrial-fibrillation/heart-palpitations-overview#1
Do you have a regular doctor you can go see?