Both are fine. Just don't ever use "up".

Hope all is well on your end

Both make sense, tbh. And both would be natural. You could not say 'at your side' because it would be taken to mean literally a the side of the person you are talking to (is your son standing at your side). the idiom relies on creatting a picture of the thing that separates you and the person you are talking to. E.g on your side of the phone call. With end, you can be on the end of sth, or at the end of sth so either works at our end of the cal, or on your end of the call.