I believe that mess with is derived from the Latin verb Mittere in the reflexive form because in Spanish “to mess with someone” is “meterse con alguien”, to put/place yourself with someone.
I think you’re saying that since English ‘mess’ shares meaning with Spanish ‘meterse’ (and shares some pronunciation) then it would also share etymology. That would be a mistake, because two languages can come up with their own words for a thing separately.
Next step for you would be to find a good source that backs up your idea.