You're doing good. I've never taken private lessons,i'm in a school band. You may be be getting dizzy because your embouchure was too big. Just make try to make the hole where you blow from smaller. It happened to me, thats what my band teacher told me, and it worked.

When i started to play the flute i couldn't even go note to note.... and yes some people do get dizzy (i still get dizzy playing really high notes form time to time)just keep to it and try to get an teacher.