Does anybody in your family (grandparents/father) experience hair loss?
Your mom is right in thinking nothing is wrong, as currently there really isn't. Walk past 100,000 people, not one would say your bald/balding. I prefer to take a more proactive approach, so if you suspect something is up, get a dermatologist to confirm/deny it. Then start a hair loss regime based on their findings.
My first post is what id personally recommend for treatments, but like i said in that post it's a LIFELONG thing, so you better be damn sure you are thinning first (Thus the derma). Why I personally suspect that you MAY have issues in the future is at 22 seconds into the video you posted the hair gap seems a bit larger than i personally expect a 14 year olds hair to be, though I honestly cant say with any certainty as i genuinely have no f*****g clue what a 14 year old boys hair gaps should look like.
As Unlucky93 said, you do not need your mothers permission to book an appointment, it's not like its some invasive surgery.