Congratulations! Sorry you are having to deal with our awful health care system. I was in a similar boat last year, pregnant & uninsured. Not sure what region you are in but here are some suggestions:

Planned parenthood is a good resource to try. If you go thru them or get referred by a nonprofit provider, the radiology practice that does the ultrasound may reduce or not charge you. I used a midwife practice here in DC (the out of pocket cost for the ultrasound normally is about $900 bit I didn't have to pay.)

You can also call hospitals but you may get a facility fee tacked on. Also expect lots if hold time with the billing depts just to get a price. Maybe try to get in with an outpatient radiology practice. You will probably need a referral.

Don't worry if it's not 20 weeks on the dot. I had that one at 18, it was fine. They should do the anatomy scan with this one, measure all of the bits carefully

Also consider getting the new blood screening materniT-21, it's a fancy DNA test that checks for all kinds of things. Much less invasive than a potential amnio but read up. The test is pricey, about $700 in all but IMHO worth it for more peace of mind. This is one of the companies:
MaterniT21™ PLUS NIPT | Info for Providers

Feel free to PM me or hit me up on FB if you have any other questions. We finished our RTW last October & our daughter is now 4 months old

Good luck!

Si Kailian