We have some storms rolling through tomorrow that have the potential to create isolated tornadoes, and I can't stop obsessing over it. Every time I see that we have thunderstorms in the forecast, I religiously check weather radars and reports throughout the day. This isn't something that's always been a fear of mine, I used to love hitting the bong and watching thunderstorms. But after having a close call last year while out delivering, and tornado sirens going off in the middle of the night a few weeks ago, I've developed quite the phobia.
Tornadoes aren't SUPER common where I live, but we had two yesterday and one a few weeks ago. All of them were super weak, and they petered out after a few miles. But the fear of a gargantuan EF-5 tearing down my apartment building is a constant fear of mine when storms are in the forecast.
If you have a neighbor you can make friends with in the ground floor apartment below you or close to a stairwell exit, you can ask to wait out the storm in their hallway or bathroom. I'd keep your cat in a carrier and have some treats handy, especially if your neighbor has other pets. A battery operated radio can also be a useful item in those situations. When the sirens go off, text the neighbor and get things ready to move to whatever ground level space you can safely but quickly. Having someone to wait out the storm with helps. I once lived in a very small complex where we'd befriended all of our neighbors and would gather all of our blankets and pets into our downstairs neighbor's place and have a good time waiting it out together.