First Trimester Doctor visits

I just found out I'm pregnant on August 12 which was when my period was suppose to start. This is my first pregnancy, so I've download a million apps, looked over thousands of websites all within a week. I have two questions.... One, my last period was July 18 (the first day of my last period) how do I find out what day I conceived and how many weeks I am. Second, I called my gyn and the not so friendly receptionist said I cant make an appointment till I'm closer to 8 weeks. Is this true, 8 weeks seems so far (my appointment in the 11th of September). I just want to make sure everything is going good in there with my little peanut. Any advice, theories etc. Thank You loves!