Engineering or Physics?

I'm surprised that you don't have a strong preference. It's not like you're choosing between physics and math, which have a lot of overlap, or sociology and anthropology. Physics is a "hard science" and deals heavily in the theoretical. Engineering is the practical application of science to the real world. Do you like to deal with theories or do you like to work with practical ideas? Sure, you'll have to learn a lot of the same things, but the emphasis is different and your goals as a professional in either of those fields will be different.

What kind of engineering? There's electrical, mechanical, chemical, civil, computer, nuclear, biological, etc. If they're going to give you a degree in "generic" engineering with no specialty, I would not think highly of the university, or at least not that particular program.

The particular kind of engineering matters a lot. Chemical engineering is a nightmare for the undedicated. You have to take all the ass-whipping chemistry courses and all the ass-whipping engineering courses. Electrical engineering is probably the easiest transition for someone who is on the borderline of being a physicist, since it involves a lot of complicated math. I know zip about nuclear engineering but my hunch is that it may have that quality too. Mechanical engineering might be a good choice because it involves a lot of physics.

Do you lust after the theoretical or do you like to see things work? That's a rough definition of the difference between a scientist and an engineer.

Don't take this decision lightly, and I would caution you not to base it too much on potential income. If one of your choices were to be a poet, then of course I'd have to be a good elder to you and point out that all but a handful of poets have to have day jobs doing something else. But people who are good at physics and people who are good at engineering both make good incomes. Go for a career that you will find fulfilling. Above poverty level, money is only a mediocre substitute for job satisfaction. You will probably spend more time working than you will spend with your spouse, so make a very careful choice.

Many American universities will allow a person with a B.S. in physics to enter the graduate program in one or more engineering disciplines. You will probably have to take some extra courses to make up for the lack of background, obviously. Nonetheless if it were me I'd find it much more daunting to have a bachelor's in engineering and try to make up the missing courses in physics!

As for math, physics requires a lot of it, and good goddess astrophysics is almost pure math. So does engineering. If you want to be a scientist without being a math whiz, you'd better stick to biology.

 

In the USA you'd probably get job preference through Affirmative Discrimination. There are plenty of women at construction sites doing the physical work.

Look into the government schools. University of [state name] (usually the first tier) or [state name] State University (usually the second tier). In a large state like California there are probably twenty campuses of each.

B.A. is just Bachelor of Arts and B.S. is just Bachelor of science. (Master's degrees are also either M.A. or M.S., and two-year colleges give A.A. and A.S. "Associate" degrees.) There is absolutely no difference, they just pick a title that fits the discipline, e.g. Bachelor of Arts in History but Bachelor of Science in Biology. There's no consistency: I have a B.S. in Accounting but many schools give B.A. Same for psychology and many other courses.