Recently, my boyfriend had a positive result of herpes. Does it mean that i am also carrying the same disease? Does herpes curable?

Not necessarily... You would have to check with your doctor for an accurate result. Getting tested will give you a for sure answer... Now, herpes can be "treated" not anything curable... Herpes can re-occur anytime again after being treated.

Dosent mean you have herpes too, theres two types (herpes simplex and herpes complex, I think) would be checked at time of having a cold sore/'s (which is when its passed on usually through contact with the sore), far as I know can be passed on through kissing, sex, oral sex, kitchen utensils etc. As I understand its a virus that lives in the nervous system and can lay dormant for some time. Apparently 1 in 5 people have it in america, don't know about uk, so wouldnt get too worried if you have, saying that your boyfriend should be taking care not to pass it on, usual rules apply. Treatments just put cream on any cold sores. Wash and keep clean/dry and good general hygiene. Some people don't show any symptoms, getting run down and stress can cause symptoms.

Its not curable and most likely if you were haveing sex with him than yes you have it as well

There is no cure for herpes at this time though your boyfriend may take medication during outbreaks. It's contagious, so there would be precautions you might want to take if you are clear.
You can find more information in the links below and it would probably be a good idea for the two of you to visit the doctor or maybe even a planned parenthood near you to sit down and discuss everything so you can learn more and ask any questions you may have.
www.cdc.gov www.herpes.com