Yes, you can collect both at the same time. If you are found eligible for SS they will oRABet what you receive from WC (or a portion thereof).
For you must have been out of work for 5 full calendar months and SS has a very stringent definition of disability. WC and SS are not related in any way nor do they consider each others decisions. So being on approved WC doesn't guarantee you would be approved for SS.
Does your employer offer Long Term Disability (LTD)? While many Short Term Disability (STD) policies will not pay you a benefit if you are on WC - very often LTD will. They too will reduce your LTD by the amount of "lost earnings" paid to you by WC.
You can check out www.ssa.gov and look under "disability"