Talk to your parents, maybe they will agree to buy you some books if not everyone... some books is better than none.
Maybe instead of asking money for specific books, ask for something more generic, like a service like kindle unlimited?

I would say that if you ask once, casually, something like "have you started bookName yet?" or something, is not pushy (maybe wait a few weeks first though). I would feel you are being pushy if you ask me many times, specially if it was a gift and not a loan.

That being said... if you are gifting me a book, it will posible take me months or even years before starting it, I have a bunch of unread books on my shelves, and it wouldn't mean I am not interested in the book you gave me.