I understand that you want to avoid mixing out-of-character statements into your in-character narration. You want to just narrate IC and have that description smoothly recognised by your GM for the actions it translates into, so your GM can take care of the OOC stuff right away any get back to the IC stuff. Your goal is to stay IC and to have this go smoothly.
Right now you can't
You can't make this smoother the way you want to. You're hiding the information your GM needs to smoothly respond to your roleplaying contribution.
Your GM is responsible for translating your IC declared activity into game terms when necessary, but you're not helping translate and you haven't given her a "dictionary" so she can do it without your help.
Narrative exclusively IC is easy and natural for mundane activity and really, really hard for non-mundane activity.
When you roleplay magic or supernatural abilities, we as non-magic, non-supernatural humans have no familiar reference points to be able to recognise what you're describing.
You have to tell your fellow mundane humans what's happening along with the roleplay:
I'm casting a fear spell. Quickly plucking a white feather from my pouch, I wave it in the air. My eyes glaze to white. Suddenly within the minds of X, Y, and Z is the vision of their darkest fear reborn. Mocking them, tormenting them, slowly approaching from the deepest recess of their mind overtaking them with fear.
This is no different than any other ambiguous roleplaying description; whether it's missing information IC or OOC, the problem is the same to your GM. In a crowded tavern with a front door atop a short half-flight of stairs, a mezzanine at the top of a full flight of stairs, and three doors downstairs and five upstairs, if you said this…
I zigzag across the room, leaping up the stairs and disappearing through the door.
… that's simply not enough information for your co-players and GM to build on your contribution. Did you just leave through the front door? Did you just charge up onto the mezzanine and into one of the upper doors? Which one did you try to go through (some are locked)?
So if you want to cast a spell, say so.
Your avoidance of that is actively preventing what you want — your GM from smoothly picking up your roleplaying bid — because you're forcing her to stop, step out of the roleplaying, and quiz you as a player to better explain what you just did. Just explain better up-front and help your GM help you.
Later, you might be able to keep everything IC and skip declaring spells, but there's a big "if" attached. Only if your spellcasting descriptions are consistent enough that your GM can learn to recognise them infallibly will you ever be able to skip saying "I cast [spell name]."
If your descriptions are custom each time? Then you'll always need to say that you're casting a spell and what spell it is.
If your descriptions are consistent, then you can ask your GM if she is happy with you skipping the name and only describing the character actions involved. (Not every GM would agree — GMs already have a lot of work to do during play, and this is asking her for more work. Not every GM has the same mental skillsets either, and what you're asking will be easy for some and hard for others.) If your GM agrees, this will still take time — you'll have to demonstrate during play and tell her what spell that description matches, possibly multiple times, to build a "dictionary" entry she can use to translate your IC narration into a concrete, known meaning. Then you can start skipping the out-of-character name of the spell.
Even then, you have to do this for each individual spell. Any time you get a new spell you'll have to build a "dictionary" entry for it like this, all over again.