Will opening a second credit card lower my credit score?

Initially it will, but not significantly. As you aculate history (time) with the account it will improve your score. That's if you don't run balances over 35%. Try to keep your debt to credit ration below 35%. 50% is okay, but once you run over that it starts significantly hurting your score. Keep balances low and if possible pay balances off in full every month.