OP, don't be upset. I actually do like Stormy and Storm as well (but for a boy). I wouldn't use them but I can see the appeal.
I would just spell it Stormy. Stormy to me is a neutral, nice nature name. If you spell it Stormi it goes over into influencer-celebrity-reality-show territory. I know you are trying to match it with your name but you will still have a special connection due to the sound, I'd recommend you pick Stormy.
Another issue that I noticed when trying to find good names to go with it is that when you pair it with regular names it sounds like the description of a person with an energetic personality. Stormy Elizabeth or Stormy Kate or something are therefore not good ideas. They are sort of like Happy Chloe or Lonely Joe or something. I tried by saying them out loud and they honestly made me laugh a lot. Sorry! Stormy Elizabeth is quite comical so I would avoid it.
I think your best bet is to go with another word name. I'll try to find some more:
Stormy Autumn - I think this works nicely, I like the image.
Stormy Eve - I think this works because Eve is also a word so in combination I don't think of an angry/energetic person.
Stormy May
Autumn Storm - as someone suggested and you could still call her Stormy.
Winter Storm - Winter is getting popular.
If you go for Storm in the middle and call her Stormy some classic names work too:
Annabel Storm
Isabelle Storm
Chloe Storm
Elizabeth Storm
Elizabeth Stormy
Caroline Stormy
Joanna Stormy
Eva Stormy
It is hard to pair but it's not a bad name (spelt Stormy that is) so stick to it if you love it. Stormy is not much different from Skye or Autumn or Brooke or other word names that are/were popular, people will get used to it quickly.