Depending on how you look at it, you're in one of the most targeted demographics for new credit lines out there. You are fresh debt, in school when most people max out everything, and are most likely in the frame of mind to rely on credit. From a lender's perspective you are prime.
You likely got denied for the kind of account you tried to start. Even though you meet all requirements, the specific kind of credit you applied for could have been marketed at a rate that is low enough to appear attractive while minimizing the risk for the lender.
The kinds of cards that will accept you with no questions are low balance, typically high interest, and probably ones having service fees. All of which are a huge scam, but tend to be what you have to do if you want to play the credit game.
The credit inquiry you speak of will be recorded but will do nothing to affect the kinds of credit lines you can open at this point. In your position, the lines you will be accepted for know what kind of credit the applicants have and will adjust their rates and risks accordingly. You will just have to do some hunting to find them.
You're a student. Look for cards that tend to lend themselves to student needs. Target is a good example. Every student could live through college shopping there and nowhere else. Look into those visa cards with like $300 limits and use it responsibly for about half a year but the second you get a real card with no service fees you balance transfer and close out the initial line immediately.
I had a similar situation as you. I never used credit until my late 20s and had to run through this scheme to build enough to look viable. A year later I qualified for a home loan at 4%. It was instructed and explained this way by my mortgage broker and I'm pretty confident this method works. I started with pretty much no credit score at all.