Just found out I'm I2b1 / I2a2a

Greetings, everyone!
I purchased a kit from 23andme and was told that my paternal haplogroup is I2b1. Attempting to do some research via Google presented me with a Eupedia thread which explained that I2b1 was actually an older name for what is now called I2a2a.
Most of my family is dead or crazy or both, and the family history has turned out to be a lot of hooey. So I'm trying to research as much as I can via DNA. DNA, at least, I know won't lie to me.
My first absolute beginner question is thus:

1. Do I need to do further digging in order to find subclades of I2a2a in order to try to get a better idea of what area of Europe my Dad's line originated in? Or is I2a2a the final word?

Thanks in advance to anyone willing to steer me in the right direction; it's all a bit overwhelming at this point.

The 23andme website allows me to browse my Raw Data and look up individual SNPs. However, using this feature, the SNPs are referenced by a long number preceded by the letters "rs" (for example: rs7892889).
I've used the information on the ISOGG Y-DNA SNP Index (I can't post links here yet) to cross-reference these rs numbers to see which SNPs show up in my 23andme Raw Data.
The interesting thing is that my Raw Data shows SNPs which show up as I2a2a (such as U250 and P223) but ALSO some SNPs which show up as being I2a2b (such as L38 and S155).

2. Does this mean that I am actually I2a2b? Or some mix of the two haplogroups (I2a2a and I2a2b)?

I'm not particularly familiar with 23andMe, so I can't really help you figure out how to extract as much from the raw data as possible, but I will say that it's not possible for you to be both I2a2a and I2a2b. It's possible that you could have a back-mutation, but 2 is extremely unlikely, so you're probably interpreting the data wrong. Are you sure that it's not just showing that they tested you at for the L38 and S155 SNPs? Because if that's all it means, you could have been tested for them, but gotten a negative.

There are definitely subclades of I2a2a that you could get tested for, but I'm not sure how deep you can go using only 23andMe. Try to see if any of your positive SNPs occur in one of Nordtvedt's 3 main groups (nicknamed "Roots," "Cont," and "Isles"; see his different "Tree for M223" slides here). FTDNA is usually the way to go if you want a very precise subclade assignment, by first joining a project with STR results and then testing individual SNPs based on administrators' suggestions, if necessary.

Thanks for your reply, Sparkey!
Perhaps it would be helpful for me to be more clear about what I did...
1. 23andme told me that my paternal haplogroup is I2b1. Eupedia helped me to figure out that they really meant I2a2a.
2. I looked at the ISOGG Y-DNA SNP Index page and noted the "rs" codes which they listed under the I2a2a Haplogroup. (each of those rs codes is referred to as a "RefSNP ID."
3. Each of those RefSNP IDs corresponds to one or more SNPs. For example, rs17316910 corresponds to both S119 and P220.
4. I then checked each of these rs codes against my raw data on the 23andme site. I assume that what I did by doing this was to look up SNPs associated with I2a2a in my raw data at 23andme, but I could be completely wrong here.
5. As I continued checking rs codes, I found that my raw data also included some rs codes (such as rs7893103 and rs7892889, which seem to correspond with S156/L40 and L38/S154 respectively) which are listed under I2a2b.

I don't mean to be a drain on anyone's time, so I'll understand if this is too much info for anyone to look over for me.

I'll look at Nordtvedt's info next...

Perhaps in order to get the initial info I need, I'm going to have to be tested through FTDNA since 23andme doesn't even seem to list my SNPs in a straightforward manner?