Should I apply the manager position

I am the one usually cover my manger's duty when he was on vacation. My boss left for a better job offer two months ago. In the last two months, the team had operated in the manager-on-vacation mode.  I reported the team status to big boss, he seemed happy about our works. However, I had more work to do since I have to handle both manager work and my own job duty  without any componsation.

I asked the big boss, he said they were still screening resumes. My friend encourged me to apply for this position since I have the ability to do so.  I don't know what's the best way to do. Should I ask big boss before I apply for this position or just ask for pay raise?

Should I apply or just wait?

Thanks for any input.