Well, “need” is totally subjective and is therefore up to you. Personally, I think that jewelry is handled all the time, and so finishing the back looks and feels much better.
As for what finish to use, that’s again up to you. In terms of irritation, I suppose it would depend on the wearer, some people might be more sensitive than others, but a shellac, polyurethane, or oil finish is generally pretty hypoallergenic.
Masking is a whole other topic, and has been covered extensively on the forum. Search for “masking” and you will find so much information. Always search first, you’ll be amazed at what you find.
This is my favorite topic on the matter: