BIWI - no SE London storms brewing atm: my lungs provide my with an early warning system (pity they feel the appropriate response to a thunderstorm = massive asthma attack 🙄 - even more fun if things get bad enough to trigger a seizure, mwerble...)
Those things aside, I've never been good with storms. On the plus side, I now know my fear response (& full on leaping, I do a quite impressive impression of a Harrier jump-jet taking off if I'm lying down & there's a peal of thunder) is part of the superfuntimes bit of my disability where I produce WAY too much adrenaline. So I get nowhere near enough sleep, but manage to function (but feel grim); & have the most ridiculously exaggerated startle responses ever; and in something like a storm where I'm constantly being startled my brain is basically being flooded with "you are in life-threatening danger!" messages. Makes alpine thunderstorms (the sort that go rolling round mountains for hours) REALLY fun, between the back-to-back nebs & blinky bits of brainweird & then ZOMG YOUR DOOM IS IMMINENT. Silly brain...
My poor cats are very scared of thunder too, though less scared than when they were younger - they seem to have decided it is not the actual end of the world, they just (understandably, given how sensitive their hearing is!) don't like the loud noises! They will come up to snuggle with me, but they do that regardless - is nothing like when they used to run & hide & stress-groom; or if they sought me out they'd not so much snuggle with me as practically try to burrow into my ribcage... They are actually less jumpy than I am 
So, OP, I think YANBU at all. I also think it's not uncommon for people who are afraid of thunder/storms to be unable to articulate what it is that actually frightens them: it's a... primal fear, almost? It taps into something quite deep in our Being Human. Sorry, yet again, wildly inarticulate due to serious sleep deprivation. Mwerbleumph.