The style of shoes you wear depends partly on what kind of dancing you are doing. If you are studying all the social dances, then get what you are most comfortable in. If you are concentrating on something where there's a lot of close-in footwork, like Argentine Tango, or just a lot of general craziness, like Lindy Hop, then it's better to get the kind of closed-toed shoes that are appropriate for that style. If you are primarily doing Standard and Smooth, then a closed toe shoe is better, too.
If you end up getting another pair of closed-toed shoes, note that different brands have different shaped toe areas. You might have to try many brands to find the brand, style, and size that is best for you.
Good luck!