Your location says "USA" -- I don't know if that's where your family lives. In USA, being an engineer isn't so prestigious -- lawyers or doctors are held in much higher esteem. But in other countries, engineers are held in high regard (or so I've heard).
I've been in engineering even before computers were household items.
By the time I got out of school, I was so tired and bored of anything related to engineering, it was difficult for me to fake enthusiasm for any job. (In fact I looked into graduate school, but none of the schools seemed interesting.) I started to see a therapist at this time, partly because my father died, but also because of the extreme dread I felt about life after school.
The only reason I got an interview (and then hired) was that one of my professors recommended me. I filled the immediate need that the company had, and so I accepted their job offer because I had nothing better to do.
Anyway, companies that hire New College Graduates (NCGs) understand that you'll need training and mentoring. They like the NCG because the NCGs haven't learned any bad habits, and the companies can offer lower pay. So in this regard, you may be more desirable than "people with more relevant experience in the field."
I hope that this response gives you some encouragement, even if all it does is assure you that I've felt this way too.
Good luck!