Sheaby, even if there were not an issue of someone's medical expenses falling on everyone else, she is also sentencing herself to a life of free clinics with spotty care, or no care at all. OP -- pregnancy stresses the body, and the body can't do things when pregnant or fight off things when pregnant that it can at other times. If you got in an accident, or a serious illness, or any number of other things including miscarriage, those things would need medical management and would not be covered by the money paid to the IVF doctor. Also, if you have cysts, possibly medical insurance would cover their management, and if endometriosis needs to be removed, the same might happen, even if they were there beforehand. (Unlike pregnancy, smaller things are sometimes not ruled out by pre-existing conditions clauses.) My regular medical insurance covered a lot of stuff I needed in the run-up to IVF even though it did not cover IVF, and it saved me money on IVF.
I agree with AnnieBrooke, you should definitely seek out Health Insurance before attempting to get any type of surgery or get pregnant. Health care costs are continually on the rise because so many people that don't have insurance can't pay their medical bills already. Unfortunately, that also means that those of us with health insurance also have to pay the price. Please, get insurance before continuing with your plans to conceive. Your child will need insurance as well.
If you don't have health insurance, don't even think of doing IVF. The $12,000 rate the first guy quoted will buy a lot of health insurance. If you get pregnant without health insurance, it is not covered (as a pre-existing condition) on many policies so you can't run out and buy some if the IVF works. Even simple complications can put you many thousands of dollars into debt. Even in an uncomplicated pregnancy, you will need to go to prenatal appointments and have gestational diabetes testing, and all sorts of other needs can arise. I just had one blood test that wasn't covered by insurance, and that single blood test cost $250. Then what if you need a C-section, or it is twins and you have an early delivery? Most good health insurance provides well-baby coverage, and you'd really need it.
After your health insurance is in place, I'd make an appointment with the regular ob-gyn and see about the -- is it cysts, or is it endometriosis? If cysts, it's possible that birth-control treatment would make them go away. Get a consult about the state of your ovaries from someone who is not also an IVF person. Then go from there.