"Amen" is not necessarily a word attached to a bracha - i.e. - ones starting with "Baruch atah Hashem...". Some examples:
When you are practicing laining parshat Ki Tavo, and you read Devarim 27:15-26, you are saying "Amen" 11 times.
Have you answered "Amen" when someone gives you a bracha (e.g. - a rebbe or friend wishes you and your family long life)?
If you are saying "Amen" in these situations, I don't see that saying "Amen" while you practice laining should be a problem, in any situation.
With regard to your concern that "sometimes the ba'al kri'a gets the aliyah", I hear you, having been a Ba'al Kri'a, myself. I occasionally get an aliyah, and I sometimes make that mistake - not the worst thing that can happen. Personally, I wouldn't worry about this, as your being called for aliyah is probably a small percentage of the time. If you do get called, daily, e.g. - you're the only Cohen, then, chances are, you've developed the habit of knowing NOT to say it, anyway.
Suggestion, that I've heard from a Rav who is also a frequent B'al Kri'ah: Don't say "Amen" out loud, as it gives listeners the impression that the word "Amen" is part of what's in the Torah, when in fact, "Amen" appears in the Torah only 13 times. (You can verify this, and edit if I'm wrong.) Same idea applies when saying "Chazak, chazak, v'nitchazek" - Look away from the Torah when you say it.