I graduated with an interior design degree a year back and then I had a late realization and decided to shift my focus towards graphic design and illustration because that's where I really see myself growing. Now I'm trying to apply for an internship for a graphic design job and was wondering about how I could mention about the field change on the cover letter. Any advice?

If you just graduated a year ago, you don't have a career yet to change. You have decided to change your focus but do you have education related to your intended new career? Interior design and graphic design have as much in common as cats and pickles. An interior design degree will not be very relevant to graphic design. Yes, both are design but graphic design requires knowledge of sales and marketing and media, print processes, types and fonts, papers, web design and many other things that are not related at all to interior design.

Are you in school to pursue a new degree?

As for how to explain it - I wouldn't unless you get an interview, but your resume needs to show that you have some relevant knowledge and are doing something with your schooling to shift your focus.

Hopefully some of your education transfers to graphic design! Specifically in types of software you used. That's what it's all about these days.
I imagine that having a small portfolio of designs would be more than half of your resume, even if some of them are interiors.
I trust that you are creative and artistic, with good ideas. I can imagine an interview involving a walk around the company, and an artist asking you what your ideas might be for a design, and how you would put it together on a computer. Do you feel that you have the quick mind for innovation? You'll need it.
But I wouldn't get bogged down. Just APPLY sooner rather than later.

Like joypulv implied, seems like the best of two worlds -- your artistic self at its best! Honor and promote both of them!

You only show them and explain to them, why you would be good for the position, no need to start confusing them with explaining anything, other than you good points.

@dontknownuthin Yes I have been self teaching myself whatever I possibly can, every information is out there on the internet but nothing beats real work experience. Most of what I have in my portfolio are pretend projects so an internship helps. Are you a graphic designer by any chance?