First time snowboarding. What went wrong?

Well today I tried snowboarding at a resort and had 4 lessons prior and still fell a million times or at least that's what it felt like. Every time I tried to get back up on my board I'd eat snow. I am 16 years old 6'3 and 190 LBS.My shoe size is a 14. I rented out my equipment, and the boots fit well but my one question would be what size of board should I have been on? I was on a 155 Burton not wide when the people from the snowboard lessons said I needed a wide board and around 162-163. But when I rented the equipment the guy didn't ask me what board I wanted, he just handed it to me. So this led to a very unwanted experience. I fell on my wrists and arms very badly making them VERY sore. After the initial damage was done from falling so much I fell more which increased my damage to my arms/wrist. After that fear instilled me from the point on I was scared to go fast at all in fear of breaking a bone.I had the basics down but I was bailing every time I got up onto the board. Should I have just gone fast from the start? Or was it my fault because of me not exchanging my board for another. I definitely want to keep pursuing this sport because I love snow and the winter plus all my friends are amazing at it.