He agregado esto en la cláusula where y parece estar funcionando
WHERE
'$myid' IN ( senderID ) AND senderdelete = 0
OR
'$myid' IN ( receiverID ) AND receiverdelete = 0
Código actualizado completo
$query_messages = mysqli_query($link,"SELECT
PreQuery.*,
m2.message,
m2.senderID,
m2.receiverID,
m2.senderdelete,
m2.receiverdelete
from
( SELECT
if( m.senderID < m.receiverID, m.senderID, m.receiverID ) as Person1,
if( m.senderID < m.receiverID, m.receiverID, m.senderID ) as Person2,
max( m.messageID ) as LastMessageIDPerChat,
max( m.date ) as LastMessageDate
FROM
messages m
WHERE
'$myid' IN ( senderID) AND senderdelete = 0 OR '$myid' IN ( receiverID) AND receiverdelete = 0
GROUP BY
Person1,
Person2
ORDER BY
m.date ASC
LIMIT 10 ) PreQuery
JOIN messages m2
on PreQuery.LastMessageIDPerChat = m2.messageID ORDER BY
date DESC");
$row_messages = mysqli_fetch_assoc($query_messages);
$totalRows_messages = mysqli_num_rows($query_messages);