This is a common snafu when it comes to balance transfers. Unfortunately, there's no way to know if your credit limit will be able to accommodate the balance you want to transfer until after you open the card. But generally, higher credit scores often get larger credit limits.
For example, some cards come with a credit limit range -- say between $500 and $2,000 -- and your credit score determines which end of the range you receive. In other cases, lenders will use a sophisticated system that considers credit scores, income, debt-to-income ratio or other types of scores to determine your customized credit limit.
This all means that your credit card issuer gave you a $500 limit because of your credit score, which was hurt by at least two factors: the two new credit cards and your utilization rate.
New credit makes up 10 percent of your credit score. The FICO credit score considers credit report requests from lenders to complete your application -- called hard inquiries -- that occurred in the last 12 months. Multiple hard inquiries often indicate a higher credit risk. The fact that you opened two cards in a short amount of time certainly didn't help your credit score.
There are important caveats to understand regarding inquiries. The FICO credit score doesn't consider so-called soft inquiries, such as when a lender pulls your credit for prescreening or account reviews or when you pull your own report. The score also allows for rate shopping and considers multiple mortgage or auto loan inquiries in a 45-day period as just one inquiry. The rate shopping isn't applied to credit cards though -- each of those applications submitted is considered a hard inquiry.
Inquiries aside, the bigger factor hurting your credit score is your current balance of $2,100. That balance raises the percentage of available credit that you're using, also called your utilization rate, which influences your credit score even more than hard inquiries. Right now, you are using 84 percent of your available credit on the card with a $2,100 balance. Ideally, you want to keep your utilization rate below 20 percent.
Closing the second credit card won't negate the negative effect of the hard inquiry on your credit score, and it probably won't help negotiate a higher credit limit on the balance transfer card. It's a long shot, but you can request a credit limit increase from the lender, but most don't offer increases unless the account has been opened for some time.
Otherwise, transfer the $500 to the new zero percent APR card and work on paying it off during the interest-free period, while also paying more than the minimum on the remaining $1,600 on the other card.
While this isn't the ideal outcome, you are saving interest payments on $500 at least. You're better off than before. Good luck!