First, I'm happy to hear that you're feeling better. Moving to a foreign country is obviously going to be a big adjustment, and it can definitely be a roller coaster, especially with an illness. Hang in there, we're all rooting for you!
I am applying for my NINO and am looking to find a job...anykind at this point just to get me out of the house and let me live a little bit. I have been doing the stay at home mom for almost 4 years now, and I think it's time. I have a Master's Degree from the States, so hopefully luck will strike me. 
This, however makes a few warning bells go off in my head. As you are a visitor in the UK, you are not allowed to work (even
volunteering as a visitor is prohibited). I therefore recommend that you sort out your immigration status in the UK if want to have the options of working and staying longer term.
As the spouse of an EU citizen, I believe you would have to apply for an EEA Family Permit, and there are a few threads floating around here on UKY if you do a search. I only mention this, as it may be a quicker route than obtaining Romanian citizenship/applying for a passport. (Unless you already have citizenship, of course-- it looks to me like they base citizenship on your parents' citizenship rather than just your place of birth, and I'm not sure of your full situation)