Can anger make it impossible to be a good person (anyone relate)?

No, you're being human. It's impossible to be "perfect" for one reason or another. Doesn't mean you're a bad person. You can be angry but still be good. Heck, look at Batman. He's a pretty pissy dude, but he's still considered "good". You're setting your own standard too high, but only because you want to go about being good in a way your personality wont allow for, so try a different route. There are many roads to being a virtuous person, not just one. Find one that fits with "you" better.