Welcome to the forum. Thanks for your question.
Your concerns, and that of your partner, are very common. However, it sounds like she is overreacting to her diagnosis. Congratulations to you for having an apparently analytical, level-headed response to her news -- despite your OCD!
Here is the link to a thread that goes into a lot of detail about genital HPV infections; please read it and show it to your partner:
http://www.medhelp.org/posts/STDs/HPV-Transmission/show/1522088
1) Should your partner should be telling her partners about her HPV-18 diagnosis? Not necessarily. Most likely she has an abnormal pap smear as well, yes? Many partners would expect to be told. However, once the pap clears up and outward evidence of an active HPV infection is gone, for sure she needn't say anything.
2) Partners of infected partners have absolutely no obligation to say anything, unless they themselves have been diagnosed with an active HPV infection. Doing so will not change their risk of getting it.
The appropriate approach to preventing potentially serious HPV problems is for all sexually active younger persons (under 26) to be vaccinated; for women to have regular pap smears; and for others to keep an eye out for genital lesions (warts etc) and get examined professionally if and when such things shows up. And beyond that to not worry or even give genital HPV another thought.
Let me know if anything remains unclear after your and your partner have read these comments and the other thread. In the meantime, tell your partner not to freak out! With proper care for her pap smear, this will all turn out just fine.
Best wishes-- HHH, MD