Hi Britgirl,
Welcome to the forum! It is good that you were able to get to your doctor and have them see your rash.
I'm not very confident that a blood test this early on would yield anything. What is being recommended in the early stage is a course of antibiotics.
Addressing this immediately will avoid a world of trouble later on.
Have a look through our resources listed in the permanent thread "New to Lyme?..." located at the top of this forum. You could go back to your doctor with that info in hand and confidently -- and politely! -- insist on treatment.
www.ilads.org/lyme_disease/treatment_guidelines.htmlGood luck!