First, thanks for a very honest and very brave post. I don't think there are a lot of people who would have dared write such a self exposing post, unless they were really hoping to make some sense out of what they were feeling. I'll try to be as honest as i can in return.
As you can tell by my user name I am heavily Celtic ancestry (yep, one could get more precise about that, but I won't) and i have a heavy dollop of German in their too, plus or minus a couple of other groups in there, most white. I say most because the German group my father's paternal grandfather hails from were known as "Black Dutch" and that opens up a whole new can of worms I won't touch right now. Just goes to show you "white" is as made up a term as "latino" when it comes to race.

I think it is very hard for many of us who are white to say if we are racist by someone else's definition or not. First, people in general have a way of thinking about who they have most in common with and tend to think in terms of those people as "preferrable" and others as "less preferrable". This could be anything from wanting to discuss politics of a certain tye with a person fom a known liberal or conservative background to assuming that people who simply look like oneself are the only that should be called human beings. If, for example, you have been hurt by some one who is white, and are sesitive to perceived racism in others who are white, you might pick up even very small signals of this tendency to draw to those who are like oneself and read all such signals as racism. In some cases, it might just be that, for example, if I here you are a physicist, I who have no clue of such things, might think, "I'd better find another philosophy person to talk to or I wil make a huge fool of my self." In other cases you might be right.
Then there is also that I as a white, am also by dint of rearing not always aware of all the ways that my culture and behavior is at times hurtful or negligible to people of other backgrounds and colors. Until one is in a situation where oneself is a minority, this is not always possible to even notice. It's called "blind spot" like what you would have in your field of vision, or where your mirrors on your car don't catch all the views outside the car. without the extra perspective, it is simply impossible to catch where one makes those mistakes unless someone helps you see it. When you train to be a psychotherapist, hopefully you can get help from someone who doesn't belong to you own ethnic group to help you catch some of your blindspots before you go out and really botch things
Finally, it's a generally human problem I think. It's one i have to work on all the time, and one that I find almost everyone whom I meet who takes such things seriously and is aware of them has to watch. Race isn't always what sets everyone off; some people get going on sex, or religion, or gender, or even weight. My weak point is middle aged women of a certain personality type. if I am not careful, I start thinking I know all about them, when actually, I have barely even met them. In doing so, I can be very, very unfair and hurtful. When i lived at home as a teenager, race was more of a problem because I still had to separate from my mom's problems about it. Now I can recognize the reflexs that come from that part of my raising and can say with some relief that it has been a while since I have been aware of any automatic thoughts that I remember that I recognize as coming from her opinions when meeting people who come from other races. Then again, to be honest, that I recognize.
Hope that helps some what. take care, and good luck to you.