[Always *]

Well, you really have 3 choices
One is to to stick around and ignore the fact your heart broken and smile pretty and be happy for them. It might hurt more but eventually you'll recover. Now here is the problem, to me it sounds like "Tom" is a bit conflicted... He wanted "Claire", then you, then "Claire" and if you stick around it might make it easier to bounce back to you thus causing you even more turmoil. But if you know that he's not likely to do that, then you can ignore the heartbreak and just try to focus on being happy for them.
Now if you don't want "Tom" to try to come crawling back (thus potentially hurting you again) or if you can't handle the heart break then you need to go with options 2 or 3.
The next thing you could do is just flat up tell them how you feel ("Tom" OR "Claire" OR both of them). Tell them that while you are happy for them being together you are still devastated by the fact that Tom chose "Claire" over you and that you need them to understand that your close to them and it hurts that their happiness has to be at your expense and you just need them to realize how you feel and try to be more understanding towards it. Let them know your trying to get over it but you'd appreciate it if they could try not to be to mushy in front of you. If you don't feel like you can put that on them revert to suggestion #1 OR move to the 3rd idea.
The last thing you can do is simply distance yourself from them for a while, focus on other friends and try to move on, go back closer when it hurts less. This way you don't have to suffer in silence OR tell them what's going on for you if you choose not to and you don't have to bear witness to their lovey dovey crap. It also might help to just see either "Tom" with no "Claire" OR "Claire" with no "Tom", this way you don't have to bear witness to it BUT you don't have to cut them out.
What you do is up to you, but the key thing is obviously to try to move on. Tom seems to be pulling on your heart strings and while I am sure he's a great guy you deserve more, hold out for the guy who will make YOU the priority NOT the second choice. You deserve more and you deserve to be his #1 choice, so do what you have to do to move on. And how you do that really depends on you. If any of my suggestions help then I'll be glad.