I think this is one of the most basic and challenging questions in your decision pipeline. Since I have no great or easy answer for this question I thought I would point you at a number of websites that might shed some light on this for you. Part of the difficulty with this question is that it is really two questions disguised as one. One part of the question is about finding out what engineers and physicists do (mayber for starters why they are so often lumped together). The other, more important, part of the question is whether these careers/programs might be enjoyable, challenging, and fulfilling for you as a human being. I make no big claims for the sites I have located (I hope they are still there when you come to use this site) but I will trust that you find them useful at some level.
Engineering
This link (http://www.asee.org/precollege/) is aimed at students just leaving or about to leave high school for with interests in engineering/science/technology. Its basic but covers a lot of bases and has good information.
I know this site (http://www.nap.edu/readingroom/books/careers/contents.html) is supposedly aimed at students trying to decide about graduate school but its actually very appropriate for undergraduates. The parts about evaluating career choices seemed very well thought out to me. I found the links describing the unexpected careers students ended up in from their starting points really interesting.
Women are in high demand in engineering for various reasons. Here is link to a site (http://www.andrew.cmu.edu/org/swe/guide/alongtheway.html) which looks at women in engineering and some of the misconceptions that exist. There are links from this site to the national organization (Society of Women Engineers) along with other useful information. Be aware that we regularly send women on to engineering schools
I thought this was an interesting site (http://www.ecs.csus.edu/career/why-ecs/index.html) that walks you through some of the decision process for becoming an engineer. See what you think.
If you run out of links to explore here's a site (http://www.careercc.com/eng.shtml) with more directions to try than you can shake a stick at. I haven't had a chance to work through many but the ones I've looked at were good.
Finally here is a guide (http://www.engin.umich.edu/students/advising/choosemajor/) from the University of Michigan to the various disciplines of engineering.
PHYSICS
Finally here is a guide (http://hendrix.uoregon.edu/~dlivelyb/UOPhys_UGrad/index.html) to potential physics students from the University of Oregon that explores why you might be interested in physics along with lots of other relevant information and stories.