Lyndan,
I understand your frustration, anger and that you're probably very very upset.
The dublin the Heathrow route frequesntly 'misplaces' bags. It happened to me twice last year during the terrorist 'upsets'. and leaves you feeling totally lost!
I'm guessing that you flew Aer Lingus to Heathrow and then transfered airlines to Sing Airlines.
Aer Lingus are not very quick on passing your bags over to another airline and the truth is Sing Airlines have no idea where you bags are, last christmas when I called BA about my missing bags I got 4 different stories from 4 different employees. Heathrow also does not have enough baggage staff to manage an airport of that size and the number of bags that need to be transfered terminals.
When you arrived in Singapore and your bag was reported missing you should have recieved a claim number, ours was with Baggage Tracer.
Try calling the airport where you landed, they would be responsible for your bag when it arrives and dispatching it to you.
As for who to claim from, I believe that there was some sort of Montreal Convention about missing bags. Again when you recieved your claim number from the airline they should have also provided all of this information as well. Have you tried looking on the airline's website for what to do if your bag is lost?
I completely understand your frustration, especially as I remember you're taking a big leap moving to Singapore in the first place!
I wish you the very best of luck with your lost bag!
AD