<p>I am sorry if I diverted the OP’s thread into something not helpful. Here is the best advice I have. First of all, a research project is most likely going to be pretty time consuming. The OP already said she is very busy and she also has a job. Considering this, I think it’s unlikely she will have time for a research project, but might be able to line something up this summer, if she doesn’t need to work a lot of hours this summer. If the OP can think of a good idea for a project that interests her, fantastic. If she can’t, just identify areas of interest and contact people working in those areas. Convince them that you are interested in their field, responsible and hardworking. </p>
<p>As far as the Olympiads go, it certainly doesn’t hurt to try to get the school to offer them. For a prospective EE who thinks she is good at physics, I noticed there is a physics olympiad, that might be worth checking out. Also, even if the school is totally unhelpful, OP can check out the computing olympiad, which I learned about recently on this site. As far as I understand, it’s free and it’s an individual competition. I don’t think your school needs to be involved at all. This is assuming some programming background…</p>