You have no need to worry about the permission of the user on the list to be queried because SharePoint will return the results based on the user permission on the list.
For returning only the items created by the current logged in user you can use the following CAML query
"<Where>
<Eq>
<FieldRef Name="Author" LookupId="TRUE" />
<Value Type="Integer">" + SPContext.Current.Web.CurrentUser.ID + @"</Value>
</Eq>
</Where>"