There seems to be more than one issue here, zjw.
Yes, people are often threatened by confidence in others, and this can be intensified in a marriage when one of the two changes radically and becomes more confident as a result of those changes. If your confidence is at issue here, then what you describe is understandable. But I'm not there and I'm only getting one side of the story, so I can't know what's going on or what to do about it. The bottom line is, if you want your marriage to survive and flourish, something new needs to be tried. There are sliding-scale and income-based clinics that offer couples therapy that you might want to look into.
Radical changes also signal the changed person moving away from the previous relationship, and tends to make the other person feel insecure and often left out. This emerges with a new job, new interests and new perspectives on life, to say nothing of cutting back on shared experiences. It happens all the time.
Those other people -- friends, family, co-workers -- who are impressed by your progress and your ability to make meaningful changes in your life...none of them are your wife. They don't live with you, they haven't gone through what your wife has gone through with you while you were drinking. It's a whole different ballgame.
When you tell your wife that she's "taking it the wrong way," you are, in fact, erasing her feelings and further distancing yourself from her. Doesn't make you a bad person, but that's what she's telling you. It's only natural that she'd feel unheard and unseen, and this almost always leads to fear which, in turn, presents as anger and irritability. Most of us would much rather be angry than afraid.
On a previous thread, you talked about how you weren't ready to go through the pain and suffering you brought to your relationship while you were drinking and, as I recall, you tended to minimize that process. I don't know of any couple that can survive happily or survive at all if amends for past hurts are not rigorously confronted. As much as we may wish that this weren't so, making amends allows for growth, strength, renewed affection, trust and feelings of togetherness in relationships, while leaving past hurts on the shelf only destroys all of these things, sometimes quickly, sometimes slowly.
Sobriety, living a sober life, doesn't stop with putting down the drink and getting healthy. Most of us have hurt other people along the way, and that needs to be dealt with in a mature and caring manner. I think the best thing you can do right now, and since you can't find a way to get yourselves to therapy, is to revisit making amends with your wife. Not only will making amends reduce her fears and allow her to feel that she's still important to you, but it will allow you to move forward with your sobriety and with your life in ways that you cannot now imagine.