I ovulated on 2/20. Doc did a blood test 2/24. Isn't that too early to get a accurate result?

I got my period 2/7. I am on the pill but was taken off two weeks early last month. Around 2/16 I started feeling weird. I thought I had a ovarian cyst (known to get those). I got a ultrasound on 2/20 and the tech said I had a dominant follicle of 1.5cm and that I was ovulating. Today my doc gave me a blood test to check for pregnancy. I am not due for my period until 3/6. Isn't it to early too get a accurate result?