YES - you do need to protect yourself. From what I've researched, the number one thing is to have everyone wash hands frequently... or get some of that foam type stuff they have at hospitals.
So far, I've had one cold on chemo, and it sucked.
Did your team give you instructions about monitoring your temp etc...? If you have a fever above 100.4 deg F, then you are meant to get yourself to the clinic / ER asap. With us, infections can move FAST, and we do need to be careful.
I have a nine year old, and we have been instituting careful hand washing in our house. I also have him use the disinfectant hand foam. And I also use the foam myself. In my office, I ask everyone to foam in, unless I KNOW my infection fighters are in strong force (i.e., have a recent blood report telling me that my blood is thick). Also, in class, I ask my students to foam in. No one seems to mind. In fact, I've only had one person say, I'm not cool with the foam, but I'll just run down the hall and go wash my hands carefully.... Great - I said - I appreciate that!
My onc team is telling me to keep away from sick people as much as possible. I'm a professor at a major university, so this is not so easy, right? Plus, I have the germy 9 year old. I love him dearly, but he's a little too free with his germs, if you know what I mean.
So, my thoughts are that you consider getting some of that hand stuff (personally, I don't like most of them - too smelly).. and get people to wash hands frequently... and keep your adult daughter at an arm's distance but very very close to your heart. Perhaps no hugs/kisses for a few days. It's not easy... but it'd be far worse if you got the flu!