This post nails it in one.
Look OP, I know you're wringing your hands because you just want your DC to have the very best that life has to offer but life just isn't like that. You make the very best of what you can offer, and maximise opportunities that you think would help your DC to thrive and grow.
Of course private schools are better equipped and funded. I know two girls who went to private school and hated it. There were lots of eating disorders and bullying, so much so that one girl begged her mum to leave to go to a state school with her friends. She did, she was so much happier, and she got amazing grades.
Obviously this is just one school and it's anecdotal, but you need to consider the fuller picture. Money isn't everything and there's plenty you can do to provide your child with a wonderful life and rich experiences, even if you can't afford the most luxurious option.
There will be people looking at what you offer and wishing they could offer their child what you have. I have two DC, both disabled - my DS is still in nappies at nearly 15 years of age and won't ever live independently. This isn't a race to the bottom, but I really do want to emphasise that I understand better than many how comparing your child, your opportunities, and your life to others will only lead to envy and disappointment.
Encourage your DD to go to clubs and make new friends - Brownies/Guides, drama clubs, volunteering, after school clubs, youth clubs? Music groups/youth choir? What are her passions, her interests?
A loving home and a present and engaged parent are worth more than all the riches in the world. Don't sour things with bitterness. Instilling your DC with the attitude that they can do anything they set their mind to is invaluable.
I know you're worried about the experiences she's having now, but all of the above will give her a rich and wonderful childhood. Seriously, don't compare your life to anyone else's - it rarely, if ever, helps and honestly, it's just a pointless exercise.