Can I get a high limit credit card if my credit score is above 717?

I have had a secured credit card to establish credit (as i am a new college student, so its normal to not have a credit history) for 6 months now and my score is 717 (or above since I haven't checked recently). I paid all my bills immediately. Do I qualify for a high limit unsecured credit card or at least an unsecured card? I'm afraid to try to apply since that may lower my score especially if I'm rejected. Thanks!