I'm not an expert, but I've read a few things, here are a few ideas…
First, try at least one additional anti-malware app.
Second, check the USB devices. The keyboard is almost certainly connected by USB (internally if it's a laptop), and all USB devices see all the USB traffic. Either someone added a little USB device, possibly between two good USB devices, or one of the USB devices she purchased had malware in it.
There was an incident a few years ago where a worker at a factory that made battery chargers that connected by USB put malware into the device, so buyers introduced malware when they connected a fresh-from-the=factory device to their computers.
As for workarounds, if you have a keylogger someone, presumably malicious, gets to know everything you type. So don't type anything. browse, play games – ones that don't require passwords, but simply do not do anything important on a computer you don't trust.
As for who introduced it into the system, if it's a physical key logger you need to look at physical access, and maybe fingerprints. If it's software there's no way to know, and the information may not be useful anyway. If it came in attached to something else the sender may well not have known it was there, and the real culprit is some slimy guy in Russia who never heard of you anyway.
If the only symptom is email and texts going to the wrong place it may simply be user error or a bug.
If there really is a malicious key logger on the machine you must get rid of it and then change every password. Every single one. Otherwise the bad guys have your accounts.