Since Drush does not run as a daemon, it is very easy to install it in your shared hosting account.
First of all, uninstall Drush 7 if you have it installed. Removing the .drush folder is enough.
Then download latest stable release using the code below:
Test your install:
php drush.phar core-status;
Make it executable.
chmod +x drush.phar;
Rename to 'drush' instead of 'php drush.phar':
mv drush.phar drush;