Here are instructions for installing exiftool on a shared Bluehost account. Thanks to https://exiftool.org/install.html#Unix for providing the instructions.

How to install exiftool

Log in to your server via ssh. Then download the exiftool distribution:

wget https://exiftool.org/Image-ExifTool-11.93.tar.gz

Unpack it:

gpack -dc Image-ExifTool-11.93.tar.gz | tar -xf -

Delete the distribution file:

rm *gz

Open the unpacked folder:

cd Image-ExifTool-11.93

Install exiftool:

perl Makefile.PL
make test

The installation and test process should take a few minutes, after which exiftool should now be installed.

However, if you try to run exiftool now, you'll get the error "exiftool: command not found". That's because you don't have sudo access and so you can't really finish the final installation steps. However, this is a way to overcome this: set up an alias in the .bashrc file.

How to create an alias for exiftool

To set up an alias for exiftool, open your .bashrc file:

vim ~/.bashrc

Add this line to the bottom of the file:

alias exiftool="~/exiftool/exiftool"

Save and quit vim:

:wq

Finally, log out of the server then log back in.

You should now be able to run exiftool as normal. For example, to get the metadata of an image, you can do

exiftool image.jpg