It's possible to have acute and chronic inflammation at the same time - they're basically different types of inflammation. In a nutshell accute inflammation is the early, rapid stage of inflammation and chronic inflammation is the later, more chronic stage of inflammation - chronic inflammation can go on for weeks, months or years.
It's kinda technical but this sums up the difference in a handy table form.
/virtualmedic.files.wordpress.com/2012/01/differences-between-acute-and-chronic-inflammation.pdf