Bro Binance is good choice
Who said you that Bittrex is not accepting new account?
I created my account on Bittrex few day ago. They opened New Account Request form and their you have to put valid reason to open account and they will open it in few days.
There is the link https://support.bittrex.com/hc/en-us/requests/new?ticket_form_id=114093958552
First support they create support ticket and then after few days they send you information regarding new account.
Say him to fill the form as soon as .