does shower count like ghusl??

HI I had to do ghusl, because i want to start praying again. So i did a shower, and i thought i was doing the ghusl correctly, but i started with Washing my awrah, then "throwing" water 3 times on my right/left side, then i did the wudu. And also i didnt say bismillah because i was in the bathroom. If u can tell me if it still counts like a ghusl or if i have to re-do it and how, because on internet there are so much "types/ways" to do it correctly. Thank you for Reading (Sorry for eventual grammar's mistakes, i'm not english)