How to search through Query Results

Hi, I am new to WP, and recently began my first page.

Anyway, I have generated a php page to pull a list of titles from a database. This works great. However i need some way to search within the returned results other than using ctrl+F. Every search module i try just turns up the page containing all the titles, or worse returns nothing at all.

Is there some plugin or search widget that will allow me to search my database results? or is there an alternative way i should be doing this?

Really I just want someone to be able to type in a name and see any titles that contain that name.