Good luck, Warped9. Sorry to hear you were let go after 13 years but at least six months severance will give you some breathing room. And sorry to hear about your father. All the best to both of you.
I'm sure you've checked with EI by now. If not, I'm pretty sure you will have to wait until your severance is gone. A few years ago I received two months severance and wasn't eligible for EI until it was gone. But then mine was classed as "salary continuance" so I'm not entirely certain if EI views that differently than severance.
And hopefully you find something much better than what I recently took as a survival job. They promised me the moon and the stars during the interview but the reality is anything but. And a little online searching recently revealed my employer has a less than stellar record for how employees are treated. Still, I keep the job because down here in London, we have the highest unemployment rate of the larger Canadian cities. We're at 9.6 right now so I just grin and bear it for the present.