Could I ask which direction your rumination takes? It strikes me that it could focus on one of two possible things: yourself, or your relationship with this particular person.
Ruminations of the first sort would be focussed on you, and would include thoughts like "I am an awful person," "nobody really wants to spend time with me," "I always screw friendships up." These ruminations would stem from very low self-esteem and generalised social anxiety.
Ruminations of the second sort would be focussed on this other person and would perhaps have the quality of a 'crush' on her - not a sexualised crush necessarily, but an intensely emotional one.
Separating those two scenarios in your head might make it easier for you to plan strategies for overcoming the ruminations.
In the first case it would be important to find ways of focussing on raising your self-esteem and social confidence, perhaps through CBT (even the basic online CBT that GPs can usually point you towards).
In the second case, it might just be a case of giving yourself plenty of distractions ('catching' yourself when you are thinking about her, and diverting your thoughts, and just waiting for the crush-like quality of your thinking to die down (as it usually does if not fed). You could also ask yourself whati is missing from your actual social connections (with partner, family and other friends) to make you obsess about this particular person.
(I don't think that citing 'rejection sensitivity' is very helpful, by the way, as it is essentially just another set of words for stating your distress. It doesn't offer anything more than that.)