Since the beginning of this school year (august 2021) my…

When she has these episodes, how long do they typically last?

How often is she vomiting in the 1-2 days the episodes last?

It would also be important to know what kind of vomit (undigested food, dry heaves, etc).  How are her bowel movements and does she have pain with vomiting?  Like stomach pain or headaches?

Without knowing more, I would say it was unusual for a child to have repeated stomach flu every 2 week for as many months as you describe.

Has she had any weight loss or fever?

It's a good sign that she hasn't had weight loss or fever.  Does she have a good appetite between episodes?

It sounds like you may be describing cyclic vomiting syndrome.  Sometimes it goes by the name abdominal migraine because it is related to the blood vessels contracting and dilating as they do in a migraine headache.

https://www.mayoclinic.org/diseases-conditions/cyclic-vomiting-syndrome/symptoms-causes/syc-20352161#:~:text=Cyclic%20vomiting%20syndrome%20occurs%20in,a%20symptom%20of%20many%20disorders.

Her regular doctor should check her for thyroid problems and blood sugar problems along with a thorough physical exam to be certain.

If it is cyclic vomiting syndrome, most kids do "outgrow" it and it is generally managed with lifestyle changes once you discover what triggers her episodes.

It's pretty uncommon, but not unheard of in children 3-7 years old.  In my practice I have only a few children with this issue.

Most studies find only about 2% of children are affected at any one time, but it is hard to get an exact number as so many children may be mis-diagnosed as having stomach flu or other problems.

Repeated vomiting without weight loss and with "normal" periods in between is reassuring for being a non-life threatening problem.  But she should have a thorough check up to be certain.