One very strong way to make readers feel they are in the character's head is to "borrow" the vocabulary, syntax, and rhythm of the *character*, even in third person. Read The Garden Party by Porter (short story, in lots of anthologies), and note how the third person narration changes in diction to make you feel like you are reading the pov character's thoughts. Joyce does this as well at the beginning of The Dead, where the narration switches from the pantry maid to the main character, just through word choice & a bit of syntax difference.
The big answer to your question is, start reading your favorite works like a writer (after you've read them once as a reader for the joy of it, of course!). Identify the word choice, sentence & paragraph length, syntax, punctuation and teach yourself what kinds of choices make what kinds of effects....
For your particular example, I get the sense of a woman who is a bit hysterical (polite police questioning squeezed the breath out of her?)...if that's who she is, great. If she's not hysterical, but rather inexperienced, feeling guilty, trauma survivor, shy, or whatever, choose words that will hang a lantern on those feelings, so we know with greater specificity what she's experiencing....
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Thanks, o jewel among women--an incredibly helpful insight. Whether I can benefit from what you suggest is another question, but it surely helps to point me in the right direction. If I could only look at the implications of my own words as clearly as you do!
This writing business is much harder for me than messing with paint.