I logged into a Phishing site?

Stupidly enough, I clicked on a link sent to me by a Jagex Impersonator, but I noticed my mistake straight after giving my info out and immediately changed the passwords to my RS Account.

Is there anything else I should do?

Has the phisher also gained access to my email account? Because I deleted all of the emails inside the account already.

 

Probably not unless he tries to recover the account with your ip passwords ect.

Enable authenticator

 

change your passwords lol

 

If the password you entered is also the same password used to log onto your email (or any other site), change those as well.

 

You should be fine as long as you changed your password before he was able to log into your account.