First, you have several things going for you:
1. You're at a good named school.
2. You've got a good GPA
3. You're female and in chemistry (not biochem)
4. You've got an internship under your belt.
There are two things I would recommend if you want to get into one of the top ten chemistry schools for graduate work, and they are:
* getting recommendations from a professor you worked with who is an alum of the school you're applying for
* doing undergraduate research, hopefully for that same prof.
Now, is it possible to get into a grad school without having done undergraduate research? Absolutely. Is it possible to get into a top 10 grad school without having done undergrad research? Possibly. Is it likely to get into a top 10 that way? No. Is it likely to get into a non-top-10 that way? Yes.
Now, for your professors saying you started too late in the game, that's BS. You're a junior. Use this year to get to know professors at your school, and find out who's cool. Go down to your service facilities and talk up the staff there. You'll find out who's an *Ignore me, I am a weenie* and who's cool immediately upon talking to the plumbers, the NMR facility people, and the glassblowers. Professors who treat their students poorly treat service staff poorly or like they don't exist. Professors who are kind to the staff are generally good to their students as well. Once you've decided on a prof to work for and whose research you're interested in, then take the plunge and work all summer at his lab. Summer research is the best anyway. If you really like the work, continue when you've got time over the school year, write up a thesis and graduate. If you don't love the work, then write up a nice thesis and graduate. If you work full time at the lab, you should have enough to write about.
Writing an undergrad thesis and doing research is key in getting into a top 10 grad school. Starting before your junior year may help spread out workload, but isn't a requirement like your profs seem to think.
As for your internship, it seems very useful. Are you going to get any papers out of it? If so, it may be worthy enough for you to use for your undergraduate research, if you go back there again this summer (or whenever it is that you did it). However, I would suggest working with a prof at the school and doing work there if you are not publishing anything from your internship.
I'm at Berkeley for grad school, and all of the graduate students did undergrad research. Many of them also did internships. They all had decent GPAs, and I haven't been able to find any that didn't also teach while they were undergrads, though I haven't heard of this as a requirement (though it certainly doesn't hurt!).
This is just my 2c, of course.