You can't use 'write in' when talking about yourself. You'd say 'email me', 'write me an email' or 'send me an email'.
The 'in' part of 'write in' refers to a media organisation such as a radio or TV station, magazine or newspaper. It's a slightly old-fashioned expression going back to the days when the main means of communication was letters and postcards. Members of the public write in to the radio station, for example, to give their opinions on programmes or on current events.