Welcome to the forum. Thanks for your question.
No research has directly compared the various treatment methods for molluscum contagiosum. If there are only a few lesions, I personally favor physical removal -- currettage (scraping by a trained professional) pricking the top and expressing the core. (Brisk bleeding afterward is evidence the entire core has been expressed and that healing can be expected.) With larger numbers, freezing with liquid nitrogen is my second choice, and is often used in my STD clinic. Although imiquimod (Aldara) works, it is slower than the other methods.
As for itching, I have no advice. Normally MC doesn't itch -- so perhaps that's not the correct diagnosis, or something else also is going on. Discuss this with the STD clinic whn you see them. It might be wise to keep the area as dry as possible most of the time, especially after treatment. Less tight clothing might be a good idea, and/or use talcum powder or cornstarch in your underwear.
Although transmission to other people by towels probably is rare, if it occurs at all, it makes sense for any person with any skin infection to not share towels, underwear, etc. But I wouldn't go to the length of using a different towel for your genital area versus the rest of your body-- but perhaps it would be smart to dry the genital area last. To be honest, I have never before thought about these issues with resepct to MC.
FYI, here is another thread that discusses MC in more detail, with emphasis on sexual versus other transmission risks: http://www.medhelp.org/posts/STDs/How-did-I-contract-this/show/1197466
I hope this has been helpful. Best wishes-- HHH, MD