Hej,
You will need to contact Mojang and convince them that you own this account. Do you remember your method of payment? If your payment method was PayPal for example, you will need to look for your transaction ID on your account, after you have located your transaction ID you will need to contact Mojang support.
You can read more about how to locate a transaction ID on their
official page. Once you have located your transaction ID, depending on your payment method, you will have to contact their
support team.
I do not understand why Hypixel would ban your account because it was not 'secure' they are in no way affiliated with Mojang AB so that seems like a silly issue.
Kind Regards,
//CeppStaff
