I can really say this in a few sentences. So I’ll do that first. Then I’ll explain myself in more detail.
A Phrygian mode is not E-E in the key of C.
A Phrygian mode is a minor scale with a flatted second. i.e a scale consisting of the tones 1,b2,b3,4,5,b6,b7.

Typically when someone first learns modes out of a book they’re taught that C to C in the Key of C is an Ionian mode. D to D in the Key of C is the Dorian mode, etc.
You’re often told exactly that- Ionian starts on the first degree of a major scale. Dorian on the 2, Phrygian on the 3rd, Lydian on the 4th, Mixolydian on the 5th, Aeolian on the 6th and Locrian on the 7th.
The problem with this approach is in how the ear hears the ‘modes’.
Because if you start with C and play a major scale/Ionian mode, and then progress to D Dorian etc, the ear is not hearing D Dorian at all. It’s hearing D to D in the key of C. The ear is still hearing the key of C Major.
And it’s the sound of a mode that makes it special.
So the first step towards hearing and understanding modes it to play them from the same root note.
Use your eyes to help you find the notes E to E in the key of C.
But play a low E to provide a strong root tone. Your ear now hears E Phrygian.
Now play a big fat C and then play E to E in the key of C again.
Hear the difference?
Pretty profound really.
I like to think of the modes as soundtracks for imaginary movie scenes. What does the mode sound like? What does it evoke?
When you play a Phrygian mode can you see the hordes of desert warriors coming over the dunes in Lawrence of Arabia?
When you play a Lydian mode, can you see the dancing girl at the victory celebration toying with that 7th veil?
Or.
Do you ‘hear’ Tool when you play Locrian?
Or ‘the funk’ when you play Mixolydian?

So here’s my recommendation:
Go ahead and learn the shapes of the modes by playing them as you see them in most books, in the key of C, one after another up the neck. Just know that you’re not really hearing the modes yet. Once you have some muscle memory of how the shapes feel in your hands, learn them again from E on your A string with a low E resonating underneath.
And then play them one at a time from E, thinking of them according to this formula which compares each mode to either a major scale, or the natural minor scale.
Ionian- 1,2,3,4,5,6,7, IS the major scale.
Dorian- 1,2,b3,4,5,6,b7 is a minor scale with a Major 6.
Phrygian- 1,b2,b3,4,5,b6,b7 is a minor scale with a b2.
Lydian- 1,2,3,#4,5,6,7 is a major scale with a #4.
Mixolydian- 1,2,3,4,5,6,b7 is a major scale with a b7.
Aeolian- 1,2,b3,4,5,b6,b7 IS the natural minor scale.
Locrian- 1,b2,b3,4,b5,b6,b7 is a minor scale with both a b2 and a b5.

Once you’ve got them, sing along as you play them. What sort of movie scene do each of them evoke?
NOW you’re hearing the modes.

To reinforce your understanding of modes, try this:
Play an E Dorian. Focus on what makes it special- the Major 6, especially with the b3. Now, play it again, counting the first note as 2 and counting up the scale until you get to 8. 8 will be the root of the key, or major scale that associates with the mode. If you did it right you should have ended up with D. With D in your ears, play the mode again, but now try to hear the notes as part of D major, not E Dorian.
See if you can teach your ear to switch between the two sounds.
Try that for all the modes.
Phrygian from 3.
Lydian from 4.
Mixolydian from 5.
Aeolian from 6.
Locrian from 7.

And finally… go to http://musictheory.net/trainers/html/id91_en.html and try to hear the modes away from your instrument. Note: You can turn a scale off by clicking on the check mark. If all the modes seem overwhelming at first, try to only hear the difference between Ionian and Lydian. Add Mixolydian when you’ve got that etc.
Hope that helps.