Other than what OskooI_007 has mentioned already (definitely worthwhile to take a look at both of those), all we can really suggest here is to try appealing to EA's ToS team again. However, it may be worth trying to get a copy of the data and check the trusted devices or logins first, as the more information you can provide, the better the chances of a positive resolution, in theory.
I should mention, though, that while all appeals are handled by real people, they rarely ever provide specific details and use set-text to keep all of their responses consistent. Also, bans are not always cheating-related, things like chargebacks and communications can also trigger them, although the general reason for the ban should be mentioned in the notification.