Tobius,
Don't worry about classification unless you are going to do musical theatre/opera. It just really doesn't matter otherwise, and is limiting.
Could you do an audio example showing your range though? Your numbers are throwing me off abit, because you should be entering your break from chest/head (or falsetto depending on your ability) around F#4 (the F# above middle C), give or take a few notes. If you mean A4, thats possible, but I would need to hear it to make sure your not pulling chest up in an unsafe way.
Anyways, it doesn't really matter again. What matters is that you can sing CONSISTENTLY in that range. If you can't, drill some exercises to improve strength, flexibility, and tonality. You could either take lessons, or buy some kind of program for those exercises.