You cannot make one column as readonly if datagridview on a whole is set as readonly.
So, firstly you need to set that to
than set all the columns in your code as readonly.
foreach (DataGridViewColumn dgvc in dgSearchedResults.Columns)
dgvc.ReadOnly = true;
follow that by setting the readonly property of required column to false.
dataGridView1.Columns("ColumnName").ReadOnly = false;