I've been through the work comp system for repetitive motion injuries that eventually became chronic.
I've learned a few things from my own experience as well as reading on our wc forum...

1- your first injury was private and not comp related. It sounds like you still had some residual symptoms from that at the time of the second fall at work. "during the past 10 months I've experienced headaches and some dizziness"

2 - wc may likely try to put some of the blame, and a % the recent injuries as related to your first fall. Nothing personal , but it's how big companies & their lawyers do things.

what they will do is look back at your health history and see the other incident, what the symptoms were, and the amount of time you missed back then.

If it gets to a wc hearing, or claim is disputed, they will be playing to win.

I could be totally wrong, but don't assume anything, and don't neglect your health to prove a point that doesn't need to be proved.

Your health is the most important thing of all, so be honest with your dr and don't deny or minimize any symptoms that need to documented..

It might be good to talk with "interview" some good wc attys , just in case you end up needing one.
With the complications of the 1st fall it will be more difficult to prove all new injuries are really new, unless your dr has been taking wonderful notes all this time.