Welcome to the community. I am sorry you are dealing with this. Ovarian cysts are common and most resolve on their own although complex cysts are less apt to do so. Imaging cannot always tell the type of cyst so it could look complex and end up being some other type. Once they get to be about 7cm or so, there is risk of ovarian torsion. Being that you have two 4.4cm cysts on the one ovary, that would seem to be just as bad as one 7cm cyst as far as the risk of pulling/twisting the ovary. But at the same time, you do not want to have surgery unnecessarily since it has its own set of risks.
Like you, I had sudden onset of pain. It lasted a whole day and then went away. I saw my gyn a few days later because I'd never had menstrual problems or pelvic pain. Ultrasound revealed a large complex cyst (cannot recall the size). By the time I had surgery 3 weeks later, the cyst was 9.5cm. Unfortunately, my gynecologist removed much more than was necessary. Instead of removing just the cyst, he removed both ovaries, my uterus, and tubes (hysterectomy and salpingo-oophorectomy). I have been suffering the negative effects ever since.
If you need surgery, hopefully your gynecologist is skilled at removing cysts (cystectomy) and will save your ovary. We actually need our ovaries for much more than having babies. They produce hormones our whole lives for optimal health. If you are not comfortable with your treatment, you can always seek a second opinion. A reproductive endocrinologist may be more apt to use more conservative (organ sparing) procedures.
Let us know how this plays out. Hoping the cysts go away and you are not faced with surgery. And if you do need surgery, I hope it goes well!
Reading this took me back to 1 1/2 years ago when I had the exact same thing happen to me. It's as if I were reading my own story. In my case my cysts where only 4cm on the left and 3.5 on the right. I also have complex cysts. At that time my ultrasound scan said the could be hemorhaggic cysts. I would get the exact same pain you did. It sometimes come on the first or second day of my period. I would end up in the ER because I could barely walk. I had to hunch over and the pain was really intense. They would just give me pain meds and I would be fine the next day. I ended up seeing my gynecologist who didn't seem too concerned since my cysts where rather "small" So I figured I would be fine. Time went by and the pain would come every 3-4 months. But this time it would feel almost like a cramp that would not go away. Leaving me very sore on the abdominal area, ribs and back for a day or two. Finally last month I went to see my gynecologist because my husband and I were havung triuble getting pregnant. She sent me for an ultrasound since I brought up the cysts to her (She was my new gyn at the time, the old one left the clinic) The ultrasound came back saying my left cyst had grown and was now 10cm! My right one was now 4cm and they were not sure if it was a hemorhaggic, endometrioma or dermoid cyst. The only weird thing is that now that my cysts have grown I hardly get any pms symptoms. Before I would get a fever, thigh pain, fatigue, nausea and no apettite and a shotting pain down my leg on the first day. Now I only get sore breasts. I will soon be having surgery to remove both cysts. I am very nervous and scared but they need to be removed because they can either burst or get twisted around the ovary. I am really sorry you are going through all this. I would recommend talking to your obgyn to see what is best for you. Keep watch on your cysts and hopefully they don't grow anymore.