Just the opposite it makes you a big big tzadik
you are keeping two chumros !
1) treating eggs as meat
and 2) treating milk as meat. You see There is an ancient chumra to treat milk as meat since chalav has the same letters as cheilev. Of course it is meat that cant be eaten with other meat due to a special limud of lo sevashel but this lo sevashel doesn’t apply to egg-meat