Sounds like a solo to me... You were able to successfully take off fly around for a bit and land. The first flight was obviously better than the second, however, if the definition of a "solo" mandates that every consecutive flight be mishap free then I would say there are very few, if any, that have ever truly done the "solo". Congratulations on not splattering the plane and a sucessful solo flight. I do believe that an instructors guidance is the best way to go, but it is obvious the sim has helped a great deal. Find out the right turn problem before you fly again by yourself... Some people require students to jump through hoops before declaring "solo", but that's most likely just an ego thing...