Nobody is going to nuclear war over Syria. We might, in different times, have done so over Israel--we did go up a DEFCON notch in 73 when it looked like the Sixth Fleet was going to duke with the Soviet navy in the eastern Med.
A much, much scarier four days occurred in
November 83. I was terrified--didn't even leave the SAC underground the entire time. Even the generals had faces as gray as concrete. We were really, really preparing for war as furiously as we could. I was praying, "Jesus, stop us!"
But nothing like that is on the horizon now.
If the worst did happen, the southern hemisphere will not only be nearly unscathed, their lives won't even change appreciably (South Sudanese will hardly notice, although granted their lives are pretty nasty already).
There won't be a "nuclear winter" to any appreciable extent--that was debunked long ago scientifically. New and better computer models.
Back in the latter 70s, President Carter ordered us at SAC to think beyond the Major Attack Option and create a plan for a nuclear "Enduring Deterrence."
I was involved in that, which was pretty tough because I knew I'd be dead. But we did the calculations on who would be able to survive and where. Essentially, if you're more than 100 miles from the nearest detonation (and most will be counter-force strikes, not population center strikes) and have sealed supplies for 30 days, you can make it. Initial radiation problems will be alpha particles--dust--for a couple of weeks. Avoid ingesting it. Wash frequently, eat and drink only from sealed containers. But alpha particles have a short half life.
Life will ratchet back in many ways about 150 years. If you want to use the gun in the mouth option some time later, that's always available. But life can go on.
Don't expect a lot of warning, though. You probably didn't even realize the scares of 73 and 83 even happened.