If your export does not show everything in your composition then you are looking at the wrong view in AE or you have set elements in your composition as guide layers. The only thing exported is the Active Camera view. There are also many ways to bring an AE animation into Premiere Pro. You can add the .aep to PPro and load the comp into the sequence, You can use Dynamic Link from inside the sequence to replace footage, or you can render to any one of about 10,000 different formats for use in PPro, only a very few of which are suitable for a production workflow. You have given us nothing to go on to solve your problem. If checking for guide layers and making sure that you created your comp using the Active camera view does not solve your problem then we need to know everything that is going on in your comp and exactly what your workflow is.
When I have exported the logo, I exported the comp which is only showing the picture, not the layer at all. I did render the comp. I have a logo that includes flapping angel wings that I animated on ae. I used comp 1 as a solid, and used comp 2 for the logo. I added the expressions which are playing in ae, but when i exported it into premiere, its just shows comp 2, and its motionless as well.
I'm still not understanding your workflow. As Rick has mentioned, we don't have enough info to go on.
How long do you measure your time with AE? Days? Weeks? Months?
It sounds like you would benefit greatly from these resources: Getting started with After Effects