When I export my video it turns out glitchy

Wow, that's bad!

First of all try switching to 'software only' rendering.

under > File menu > Project Settings > General > Renderer pull down menu.

If you already have this as 'software only' try one of the other GPU acceleration options.

Then do a test export.

If that does not work ...

If you preview render your sequence do you see the 'glitchiness' in the preview render?

If not: Ensure your 'Video Previews' in your sequence settings (found in the 'Sequence' menu) are set to something high quality like Prores, DNx or GoPro Cineform. Preview render your entire sequence (check it's OK by playing back the sequence) then export your sequence and check the 'Match sequence settings" check box in your Exports settings dialogue box.

That will give you a high quality exported file that you can then encode to what ever you need using Media Encoder.

As to what's causing this: Don't know.

You don't mention which version of Premiere Pro you are running and if you are on Mac or PC.

Normally I would suspect something GPU related and if 

'software rendering' fixes the issue it is likely to be it. DPossible driver issues if it's on PC. The new Macbook Pro 16" models are having issues with Premiere Pro that might be GPU related. And more.

Let us know how you go.

Steve