What do you do if you are allergic to latex condoms? Do you just wait for the infection to disappear?
Let's take a look at your second question first. Any sort of rash or infection with unknown causes deserves some medical attention. Instead of just waiting for the infection to disappear (who knows how long you could be waiting), pay a visit to a health care provider. After examining you, s/he will be in a better position to know what is causing the infection, how you can treat it, and how to avoid future problems.
Several studies have shown that only about 1 percent of the general population is allergic or sensitive to latex. A visit to a health care provider will help you figure out if you belong to this group, and if so, what type of precautionary measures you can take to avoid future reactions. Take a look at Alice's archived answer to Latex allergies to learn more about allergies and sensitivities to latex products.
Many people sometimes mistake symptoms such as a rash or infection in their genital area for latex sensitivity, when really a separate problem is being aggravated. Finding out exactly what is causing your rash or infection is the first step in treating it.
What are you going to keep in your bedside drawer if it turns out that you are allergic or sensitive to latex? Luckily, you and your partner(s) have options. You can use polyurethane (male or female) condoms, which are made from a different kind of plastic. Polyurethane condoms also protect against sexually transmitted infections (STIs). If you and your partner have tested negative for STIs, are in a monogamous relationship, and pregnancy is a concern, you could also consider lamb skin condoms, which protect against pregnancy but not STIs. In place of dams (for oral sex), try using non-microwaveable plastic wrap, or removing the ring and cutting down the length of a polyurethane condom to make a rectangular substitute.
Since you have an infection, your best bet right now is to see a health care provider. Once the infection is under control, you can begin to investigate whether latex is your friend or foe. Best of luck,Alice!