Sorry that it didn't work out for you. I can tell you that my daughter did the same as you: applied for every kind of internship available, and I'm wanting to think that she applied for over 30. She was fortunate enough to get one, but it was not without a lot of angst and worry as it came down to the very last one that she had applied for in the process. Along with her interview, one thing that I feel really helped her was an incredible reference letter that she got from one of the folks she worked with as part of the College Program that pretty much laid out exactly who she was the skills that she had that would be to her advantage in the internship that she ended up getting. If you've done the CP, then I'd ask your leaders for a letter of reference. That type of thing carries a lot of weight.
Keep on applying, and good luck to you!
