Yes, although there is an overlap. As you seem to have figured out, "sensitivity" is pretty much the quality of being sensitive, but "sensibility" is not that of being "sensible" in most cases. "Sensitivity" talks about a direct response to stimuli, which are often physical -- heat, light, pain and so on -- although they can be emotional, too, which is where it starts to overlap with "sensibility". For example, you can talk about someone's sensitivity to criticism. But "sensibility" has more to do with emotional and intellectual perception, and often has to do with empathy. To distinguish the cases -- since we are in the middle of a never-ending election here in the US -- let's talk about some political issue that's key in the process, e.g. universal healthcare, or tax fairness or whatever you choose. A politician may show sensitivity to the issue and come up with new policies to address it in order to get elected, but without sensibility to the issue, they may not really care whether the population is getting the health care it needs, or that people aren't paying their share of taxes, etc.

Sensible(Sense+able) - this is possibility to feel sense sensitive - this is quality of someone or something(for ex. sensitive skin, sensitive sensor)

What you said is correct and their nouns are much the same . She has the sensibility to know that marrying the rich guy is better than marrying a poor guy , but she is afraid to do so because the rich fellow does not care about the sensitivities she has about certain things that she hold dear , such as not insulting her poor background and religion .