Are there any non surgical ways to shrink fibroids?

Yes. Some hormonal treatments can (but not always) shrink fibroids. Uterine artery embolization performed by a radiologist can also shrink fibroids. And now some ultrasound and MRI guided procedures can also shrink fibroids. A long action injection of medicine called Lupron (leuprolide) can also be effective. None of the procedures are recommended in someone who wants to be pregnant in the future.
Yes. There are various medical treatment options in addition to uterine artery embolization. If you fail medical treatment the next option other than removal of the fibroids or uterus is to embolize or close off the artery to the uterus which shrinks the fibroids. This is minimally invasive and can be done without an overnight hospital stay. Recovery perior about a week. Shorter recovery than surger.
Absolutely . Most patients with fibroids need no treatment. When the fibroids cause symptoms such as heavy bleeding, severe pain or pressure, or changes in bowel and bladder it is time to seek some treatment. Surgery, is the most common choice but pseudo-surgical options such as uterine artery embolization, focused mri-ultrasound beam, cryotherapy or radio frequency can help. Iud, pills, and injections help.
Symptom control. Uterine artery embolization, and focused ultrasound are two "non surgical" means to shrink fibroids. While they are both procedures, they are not surgeries in the classical sense. They both, however can be associated with significant discomfort. There are several options to try to control your symptoms, and you should consult an ob/gyn to discuss your options.