Lookup ID and if cell in row contains something show the title of that column

This sort of concatenation is a very common request and is usually solved via VBA as it usually consists of an increasing number of columns, but as you have a fixed number of Allergens (16 columns O to Y - and hopefully this will not increase) it is possible to solve it via a formula. However, I can only see a formula being possible by using 16 IFs, one behind the other in one formula resulting in a value from O2:Y2 or a null which is not very practical e.g.

IF(INDEX(O3:Y3,MATCH(A2,'All products!A$3:A$2000,0),1)="Does Contain", INDEX(O2:Y2,MATCH(A2,'All products!A$3:A$2000,0),1)&",","")&
IF(INDEX(O3:Y3,MATCH(A2,'All products!A$3:A$2000,0),2)="Does Contain", INDEX(O2:Y2,MATCH(A2,'All products!A$3:A$2000,0),2)&",","")&
IF(INDEX(O3:Y3,MATCH(A2,'All products!A$3:A$2000,0),3)="Does Contain", INDEX(O2:Y2,MATCH(A2,'All products!A$3:A$2000,0),3)&",","")&
etc
for 16 columns

Then remove the rightmost comma of the result so you dont have "Sesame, Soya, Nuts,"

Cant see an easy way of doing this via formulas.