Update:
I am able to plug iPhone into new laptop I am speaking of and actually do a back-up to my laptop. Now, when I go to add a ringtone to my iPhone, I get the message to sync it has to erase since it can only be synced to one library. Can I just do that and then restore from the back-up I have on my laptop that I just made and be back to how it was? Am I confusing things?
Bottom line, I have no media on my phone I need to save since I use iTunes match and all my photos are saved elsewhere. I just want t add the ringtone and have my phone stay the same elsewise. This is getting ridiculous. I don't want to lose my settings, I just want my phone to stay the same, just with one more ringtone. Am I asking too much?
I don't really need to sync, or need anything off of my new computer except that ringtone. Will I really screw it up if I do the erase? Can't I just restore from the backup on my laptop I just made and get all my settings and apps back in place? Contacts and all and texts.