Yes, kickboxing can work very well in the street, but you need to understand the limitations of the training. Simply put, you are training for a competition with a very specific set of rules, rules that you won't find if you brawl in the street. For example, a lot of amateur kickboxing competitions don't allow you to use knee or elbow strikes, or kick someone in the groin. If you got into a street fight those rules wouldn't exist. This is all about the mindset than anything else.
Now don't get me wrong, if you nail someone in the head with a good roundhouse kick, they will go down like a sack of bricks regardless of whether you are on the street or in the fighting ring (in fact, they will go down faster on the street since you'll be wearing shoes). Just always keep in mind that your opponent on the street is likely going to act completely differently to what you are used to in the fighting ring. If you really are worried about it, I would try and find a dedicated self-defence class that you can do alongside your kickboxing, to learn how to use your kickboxing skills in a street environment. As a kickboxer you should already have the basics of punching and kicking down, but there is a difference between using them on the street and using them in the ring.
