Connect Xbox Live to EA account for Prime Gaming Rewards

I've been trying to redeem my rewards from Prime Gaming. I have my Origin EA account (with TS4) linked with my Amazon Prime account that I redeemed skins for Apex Legends on. However, I play on my Xbox One and have a Gold membership. I tried to link my Xbox account with the account mentioned above, but when I tried to sign in with Xbox, it made a new account for me with my Xbox gamer tag. I have not played any games or bought anything on that account, as far as I know. I would just like to connect my Xbox Live account to my EA/Origin account so that I can redeem my rewards. My Xbox account and my Origin account have different emails.