Should I Worry About SQL Injection When Using wp_insert_post?

WordPress DOES take care of SQL injection and for you. See the Security section on this page. The wp_insert_post() function runs through sanitize_post().

Be aware that malicious or unintended code can still be inserted:

“You may wish, however, to remove HTML, JavaScript, and PHP tags from
the post_title and any other fields. Surprisingly, WordPress does
not do this automatically. This can be easily done by using the
wp_strip_all_tags() function and is especially useful when building
front-end post submission forms
.”

Should you not want to strip ALL tags, Validating Sanitizing and Escaping User Data is a good page to start looking for specific sanitation rules that are built in. You can never be too secure.