Hi and welcome nenvy.

As far as i am aware you do not need to have word installed to use the Outlook spell checker.
What is the exact error message you are receiving?

Make sure you have the correct configuration for the spell checker.

On the Outlook Tools menu, click Options.On the Spelling tab, make sure "Always suggest replacements for misspelled words" and "Always check spelling before sending" are checked.

This may help you here