As another one who's done a bit of both, I'd say there's *usually* wisdom in the "pick one" train of thought, as mentioned above, although your own mileage may vary...if riding in the back of the airplane is enough to scratch the flying itch, flight test engineering might be a really good fit.
I had always been interested in both flying and engineering, but I kinda got my engineering degree as partly "backup plan" and partly "because 4-yr degree" (I wasn't too bright about avoiding work, plus Mike Rowe wasn't around to convince me otherwise). I wasn't a nerd, but I did pretty well in engineering school, and I realized I enjoyed learning the concepts. I especially enjoyed our capstone design course (though it 'bout killed me--I lived and often slept at the design/mfg lab, and mostly existed as a zombie elsewhere for that semester).
Despite my initial reasons for going to engineering school, by the time I graduated I had a very marketable skill in something I'd found interesting, and a very *un*marketable Pvt/Inst. So, my options were, (a) a well-paying job as an engineer at a defense contractor where a bunch of my classmates were going, (b) grad school, or (c) spending (i.e., borrowing) a ton more money for ratings in hopes of eventually landing a poor paying flying job in the post-9/11 slump...
I chose (a)--figured I'd build an RV-8 in my garage and fly for fun. I didn't like the job, though, and wound up saving some money for a bit, then getting the rest of my ratings and going to fly after all.
I have to confess I don't often pine for a cubicle, but I think you're on a great track. I'd agree with the advice you have been given--try to get some internships and see different aspects of the industry. Try to do real work at your internships, too--the good news is, most companies that hire engineering interns do try to put them to real work, rather than just entertain them.
See if you can find work you like, and maybe even a company you like.
In the future, if you do want to try to fly and engineer, though, I would recommend exploring General Aviation. Find a smaller company, with a smaller staff, where your job might have a little less specialization, and a little more variety. Flying or no flying, you might find your work to be more interesting with some variety.
Maybe even one of the better kit manufacturers, especially if you're interested in experimental (i.e., "home-built"/amateur built) aviation at all. Trade-off there (there's always a trade-off), is likely less job stability for getting to do something more interesting.
Best wishes for finding an internship, and for your next steps!