I understand your feeling of intimidation by enterprise programming.
The internship will most likely cure it, it certainly did for me.
You will not be put in charge of projects you can't handle, too risky for the business.
If no appropriate project can be found for your level, you simply won't be hired.
Be honest about your skills. Don't lie, don't exaggerate.
'Programming for X years' means jack shit to recruiters unless you have projects that back that statement up (ideally your projects should demonstrate your evolution and progress as a programmer).
Passion. If you can prove passion and have a half-decent portfolio, you can even get away with not having a degree (I'm the living proof of this).
As long as you love programming, practice it regularly and have a passion for learning -> don't worry, be happy!
You can do it ;)