Watch the Bird Out online guitar lesson by Jeff McErlain from Essentials: Chord Tone Soloing
I start off this solo grabbing some chord tones to create a cool descending melodic line. The progression is Bb-F-C7, and the first note I play is Bb, which is the root of the Bb chord. I then lower this a half step to A to play the 3rd of the F chord. I'll move down the scale to play G, which is the 5th of my C chord. Very simple conceptually, extremely effective musically, and a tried and true approach to creating melodies.
I discovered this technique largely by thinking about chord tones, and even though these notes are contained in the C Mixolydian scale, that doesn't mean we would automatically see the melodic line. It's only by looking at the notes within each chord that these things become apparent. I cannot stress enough what an epiphany this was for me after many years of playing. Like me, your teachers have been telling you for years to work on triads.