Possible malware software on Iphone5 - how to find out?

Hello, i received an e-mail stating that after watching a video on a certain website through Safari on my iphone, a software was placed in the video and my browser started operating as a remote desktop with a key logger which gave the person access to my display and web cam. After that the software program has gathered all my contacts from Messenger, e-mails and social networks. The person was threatening me that he will send a double-screened video of me with XXX content to all my contacts. He wants money not to do it. It looks very much like spam but he quotes one of my passwords that i use for some websites accounts. My question is - is all that he says actually possible to happen on my iphone and how can i scan it to check about that software that he claims he had installed? I loged out of all my accounts on the phone and changed my passwords on the computer but now i don't know if it is safe to log in again on the phone in case there is really such software installed which copies what i tap and write. Thank you in advance for the help!