Hi,
I have been in tourism industry for a while. I have never worked for Spain until now, but I am VERY sure that I can find you more private room accommodation for that price. In fact, I will find you 5 and I will give you contact details (tel, skype, email etc) of people in Barcelona who like to accommodate. I will need 3-5 days to do that. Then you can contact them and you can choose the best accommodation for you.