It may help a bit
A second credit card would expand your history, which may help a bit to raise your score. But don’t get your hopes to high. It takes time – you will need at least 24 months of consistent, timely payment history to improve your score. Those timely payments are what actually build good credit.
Naturally, you will need to use both cards. Just having a card won’t help a bit, so use both credit cards for regular purchases, wait for the statements, and pay the balance in full every month. That will build your credit and avoid interest.
Just for your information, if the student loans are reported to the credit bureaus and appear on your credit report, they count in your credit as well. Any reported debt counts in your score.
Usually, Federal student loans are NOT reported unless you fail to pay. Private student loans are generally reported whether paid or not. The reason for this is that the government is helping you tp “hide” your debt load, so that you are not rejected for other loans because of high debt-to-income