If I am currently in a personal injury case and fell at another location while I was out for the first injury, can I still sue the new location I fell at?

You need to talk to your lawyer about the second accident as soon as possible.  What you have described is called an "intervening cause."  The significance of this is that, if you were injured in the second accident, then any claims for medical treatment, pain and suffering from that point forward become overlapped with the first accident.  This can make it nearly impossible to distguish which party is responsible for the injury claims after the date of the second accident.