First time mom

So I found out on Feb 29 I am pregnant. The lines were so faint I wasn't entirely sure so March 1st I went to the lab to give a urine sample. Had to call over the phone to get the results which were positive. I hear of so many people actually seeing a doctor right away and also doing blood work and for me the OB/GYN clinic got me an appointment for March29! They said that was all the have available. Almost a month out from when I actually found out... Is that normal? Should I call and keep asking if there's any openings sooner? Based on my last period the calculators are saying I'm 3 weeks and 4days.