I'm a community college student in san diego that is looking for an internship that is paid. It doesn't have to pay well. Preferably at a small company for 10-12 weeks. I talked with one of my instructors who works at intuit and he gave me the advice to apply to a small company because "larger companies are very picky and only take students from top schools". I'm practicing leetcode every day and learning react and django to combine with my python skills to create a resume website/programming project that I will be pushing to my github. I asked him for learning resources and he reccommened fullstackpython.com. I've come across the idea of messaging recruiters directly on linkedin as a way of getting interviews because I will most likely be filtered out if I apply directly though a companies website. I'm thinking about attending career fairs after I complete my project. Any other advice or someone with a similar experience?
I'd like to add that I've taken all programming classes for my major at my community college, the only thing i have left is the remainder of the calculus series, discrete math, and linear algebra. I know java, python, and c++, and have studied assembly.