I am not completely understanding the issue here. You have one random row from your fist table and you want two more from another table, which shouldn't be a problem. I assume you have a field in your row that contains valid symptom ids from your symptom table and I will assume that you have those in csv format (comma separated variable).
Obviously, I have not tested this, but it should do the trick.
$symptomID = explode ( ',' , $row['symptoms'] );
$selectedSymptom = array_rand ( $symptomID , 2 )
$randomized_symtoms = mysql_query(
"SELECT * FROM symptoms WHERE
Of course it may be easier to provide each illness with a corresponding 'symptom class' and a 'symptom count' so you can...
"SELECT * FROM symptoms WHERE sClass='$indicatedClass' ORDER BY rand() LIMIT '$indicatedLimit'"