Does the school that you were accepted to offer courses in engineering or the sciences? If so, you could try to take a class in that while pursuing your original degree. That would allow you to test the waters with engineering. If after taking that class, you decide engineering is for you, you could look to transfer and hopefully have fulfilled some of your general requirements along the way.
If you'd like to be economical about the situation, you could always try to apply for an internship or job in your field of interest during your year off between high school and college. However, with the job market being what it is, you might have difficulty finding a technical job. You could look to participate in a shadow an engineer program where you are able to follow engineers around. In addition to finding some job experience, I would use the gap year to take courses that are focused on engineering and the sciences. Community colleges are a great place to start with as you are able to take a variety of courses for less money than at a 4 year university. But, some 4 year universities allow for a student at large status where you can enroll in a university course without being a degree seeking student. These courses can usually be rolled over to a degree once you are accepted.
If you are set on taking a year off to look at another university, I would definitely recommend trying to talk to as many engineers as possible. If you are unsure about the type of engineering you would like to pursue, I would recommend looking online to find the local chapters of engineering organizations and attending a meeting to talk to their members about their experiences. For example, you could look for the local chapter of the Association of Computing Machinery (www.acm.org), Institute of Electrical and Electronics Engineers (www.ieee.org), American Society of Mechanical Engineers (www.asme.org).
Look at your gap year as a fact-finding mission. Engineers have to seek out facts every day. Consider this opportunity as one engineering experience. And don't forget to include your discoveries in your applications to another college.