Denied preggo bloodwork test until I'm 6 weeks?!

***UPDATE: 
You guys are amazing!!!
You were right when you said I was already about 4 weeks along. I never knew how to calculate that! So I called my obgyn office and they said my insurance covers my wellness exam. I only have to pay for the pregnancy appointment, which I was able to schedule for July 17. That's about 2 1/2 weeks away! Thanks for your advice ladies. You rock! Now I feel butterflies in my stomach 🦋 🦋 🦋😍😍😍***
***ORIGINAL POST***
So far I'm pretty sure I'm pregnant. I've taken 5 or 6 tests in the past 3 days (3 different brands) and they all came back positive and lines getting darker.
I have a wellness women's exam on July 10th, and called my obgyn office to see if they'll also do pregnancy blood work to confirm, and they told me no.
Basically they told me that they won't do any of that until it's been 6 or 7 weeks, then they can do verification. But by 6 weeks I'll be more than sure if I am or not lol.
Does this sound right for them to deny me that? They won't even let me come in to just do blood work for it. I'm confused. I just want the blood work done so I can be positive. Or can that also only be done later?
I called my General doctor, but they only do urine tests.