yep, i have an HMO and i have to have a doctor's order to get bloodwork done (i also go to quest diagnostics for all my lab work). the doc will fill out a an order or referral or whatever it's called. you take that to the lab and give it to the receptionist and they'll call you back when they're ready.
the nice thing about quest is they have an app, and it allows you to make appointments up to a few weeks ahead of time. it'll save you a bunch of time to schedule a time as they tend to have PLENTY of walk-ups. since it appears time is a concern, you can schedule for any time of the day (i usually schedule for late afternoons so it doesn't interfere with work).