Let's say I'm writing a song in Db major and I want to make a key change to make it feel higher. And I want to choose from Ab Or Gb. Why I'm asking this it's because if you see the circle of the fifth. Ab has 4 flats and Gb has 6. And in the middle there is Db.. And I am confused as to which way is actually making the song higher.
Well it seems to me, that you would choose to move in the direction you would like to go. You can modulate up or down with either of the key changes you've cited in your question, simply because there are G flats and A flats both above and below the original key of D flat. If you're writing it out on a stave, chart it above or below, whichever way you want to go, the change in key signature will not determine the octave position of key change, that is determined by the notes on the stave.
There's quite a good article on Harmonic Brightness & Darkness by Anton Schwartz, which is worth a read if you're interested in the Circle of Fifths. The answer to your question is really "it depends" - typically, you want to modulate up the circle of fifths in order to get a brighter sound and down to get a warmer or darker sound. However, you can modulate down and make the song sound brighter or modulate up and make it sound warmer or darker depending on the melody and harmony you choose to use in your new key.
Going by convention though and as a standard answer - move up the circle of fifths (clockwise) to get a brighter sound and down it (anticlockwise) to get a warmer or darker sound. By this logic, with your example starting on Db, you should go to Ab as seen by going clockwise round the circle of fifths:
I really do not think your song will sound higher or lower with a modulation, or key change such as you suggest. It's moving just about as far as it can go either way.
The bigger problem might just be that whichever you go to, the vocals may need to drop half an octave. Now, nothing will sound like it's gone up.
The commonest two key changes - modulations - that sound convincingly like the song has gone up are one semitone or one tone. Thus, your Db key wold go to D or Eb and sound very much more like it's gone up in pitch.
Trying to answer the question directly, there's a slight bias towards Gb, as Db is the dominant of that new key, but I still don't think the desired effect - going up in pitch - will be convincingly achieved. It'll sound more like the song is going into a middle eight.
And I am confused as to which way is actually making the song higher.
Any key change can raise or lower the song. Just consider the extreme case of raising everything a whole octave.
Whether it gets higher or not depends on more than just key signatures. In the extreme cases, it's easy. If you change by a half or a whole step, it's almost completely obvious what's going on. Sure, changing from C to D can lower the key, but I have yet not seen an example where it's done. So in this case it will be obvious from the mere fact that it is much closer to get from C to D with raising than lowering. The further away from the original key you get, the trickier it will be to say for sure. When you're changing a fourth or a fifth you need much more context.
Going to a Gb from Db has a higher chance of feeling raised than going to Ab, but it depends a lot on what you do with the melody.