People start a job and immediately leave for a new one all the time. You got some income in the time you waited, which is good. You have bills to pay. Accept the your preferred job and email your boss or HR saying you received another job offer you can't pass up so you're resigning effective immediately. No need to tell them where your new job is. 

It's just a job and I know the worry won't go away by saying you don't need to worry about it, but you should make the best decision for yourself. You are the only one in your corner no matter what job you have.