My classical player mate has used the services of his local nail bar in the past when a gig was looming and he had broken a nail. It works well but don't leave artificial nails on for more than a couple of days as your real nail will soften and it then takes a long while for it to recover enough to use them for playing again.
I don't play classical but do play some finger style and I don't like playing without nails, but, annoyingly, I don't get on with fingerpicks either (and I've tried loads). The nearest I've found are Alaska Finger Picks because, unlike conventional fingerpicks, they sit slightly under your nail so the tip is in the same place as your nail would be.
https://www.amazon.co.uk/s?k=aLaska+...rkbootcri01-21