Many times blackheads become infected due to someone trying to pop them out the wrong way.
First you need to make sure to wash your face and hands properly. Then you have to steam your face to open up the pores, making extraction of blackheads easier, then you can go ahead and pop them. The blackheads should come out easily, if they don't you need to stop, otherwise they can become infected.
When you don't take proper measures before trying to pop a blackhead it can easily become infected and even leave a scar on your skin.
How to treat infected blackheads?
If a blackhead does become infected the first thing you need to do is to stop touching it. Your hands have a lot of bacteria and by touching the infected blackhead you are only making it worse.
Second you need to do is to apply a special solution that will dry out the blackhead causing it to fall out, make sure it is high in salicylic acid. "Buy buy blemish" is an excellent overnight drying solution, you can find it at beauty supply stores or purchase it online. It is only $10, and is great for spot treatments.
For a natural remedy try dabbing a cotton swab in freshly squeezed lime juice and apply it to your infected blackhead. This will help to dry it out, and treat it at the same time. It might not be as strong as over the counter solution, but it is more natural and doesn't have any chemicals, which is always a good thing for your skin.