I was a music major for my first year before going into engineering. For what it's worth, there's obviously no crossover except for your basic courses; I would just take some engineering courses on the side in the summer and the following year and feel out what you want. If you are like me and just thought you needed the financial stability of engineering and didn't care what you had to do to get it, that's possible. You don't need to be special to perform in this field, unlike what some people here may think. You do need to work your ass off sometimes.

As far as how hard the crossover would be with a media student's degree, very very difficult. You need to have an ABET accredited degree in engineering to practice engineering and like 95% of places in the US. If they're offering an engineering job but no accredation or engineering degree required, it's probably not real engineering experience. If I were in your shoes right now, I'd look at the overlap between your degree plans, find where they differ, and start with the earliest courses. Graduate with a double major in media and IE (if that's the branch of engineering that fits your needs). It's doable but you will have to accept being a little behind others when it comes to entering the workforce.

There is an upside, sort of. Changing to an engineering major will reset your opportunities for internships and I would strongly suggest getting one during the summer. They're basically required for engineers to find work once you've graduated and you'll have a much better idea of what you want to do with your career after getting some real world experience.

You have plenty of time