Capitalization

You can do that if you like. It's up to you. California has to be capitalized.

CB

California should be capitalized. "Southern" is just a regular adjective, which doesn't need capitalization.
But it's important to note that names of places such as the following must be capitalzied:
South Pole
South Carolina
West Germany
Easter Island
West Hollywood

This is a tricky one. Most formal guidelines I've seen would indicate that you should not capitalize "southern" in this context because it it merely refers to part of state based on the point of a compass. Southern California is not a formal or political entity, it is simply a description of a geographic portion of one.

Still, you will often see it capitalized by local English speakers

I think the only hint possibly linking the capitalization of "southern" to California is that there was a time certain political force was trying to divide California into two separate states, much like North and South Carolina. You are right about the usage of "SouthernCalifornia". Perhpas The L.A. Times still has few remnants of that movement working there.

In fact, the Associated Press Stylebook (yes, it's one word) recognizes "Southern California" as an established region, with a capital S, putting it in the same category as the South Side of Chicago or the Lower East Side of New York.

I don't have my Chicago Manual of Style any longer; it would be interesting to read their take on this.

Formal rules and customs are important, but so is the appearance of construction. In the context of California, I always capitalize Southern or SoCal because otherwise it looks awkward. And that separatist movement for 2 California's is still alive in certain circles!

She is from southern California