What constitutes a "medical necessity" for a pregnancy blood test?

Hannah
Over the past few days, I've taken countless urine tests that have all been positive but only barely.
The second line has not progressed to be any darker than it was originally on the day AF should have arrived.
Asking around on the internet has told me that I might be experiencing a chemical pregnancy because at the very least, the FRERs that I've taken should have gotten darker since they are quite sensitive to HCG levels.
Anyways, back to my question: PP states on their website that they will only do a blood test for pregnancy if there is a medical need and I have no idea what my GP will say or even if I can get in to see her soon.
Does anyone think my case of apparently low levels of HCG count as a medical necessity? This is my first pregnancy EVER and I'm confused.
Edited to add: I want the blood test to find out the actual levels of HCG in my system. Not just to confirm what I already know. And also to add that I'm 4 weeks + 3 days.