What should i do now about my job?

I'm 17 and work part-time at p.s. aeropostale and only work 10 hours a week. For that reason, I'm looking for another job over the summer that promises me more hours. I have spoken to the hiring manager at american eagle and he is already willing to give me a job. The manager at AE had worked for aero for 8 years and knows how clingy they can be with their employees. However he was offering to give me the job if I could settle a deal between the tw. I gave notice to my manager at p.s. that I am searching for another job and put my current employment information down as a reference so it culd be verified. She told m that I could not work at another clothing store because it's a conflict of interest. I would choose the American Eagle job over P.S. and I'm afraid my manager will fire me now that I am looking for another job. Should I just quit my current job ASAP?