Usage: dismiss someone's concerns

The word that pops to mind is alleviated.

Michelle alleviated my concerns by proving to be a person who is able to successfully develop plans and implement them.

By making your concerns go away, either by being dismissed, or "erasing all doubt", to use another phrase, in the context of your example, dismiss is neither negative or positive.

Now if you had said, "Michelle was dismissive of my concerns", that could be construed as a negative comment - particularly out of context of the rest of the sentence where she is exonerated by her performace, thus "making your concerns go away".

EDIT

As jwpat7 rightfully pointed out - you dismiss your own concerns. So you might rephrase your sentence:

"I dismissed my concerns about Michelle when she proved to be a person who could successfully develop plans and implement them."

In OP's context, allayed my fears is a common phrasing.

As @Kristina says, dismissed my concerns is reminiscent of was dismissive of my concerns, so it's probably not the best choice for a context where Michelle isn't necessarily actively doing anything for the specific purpose of making OP feel more confident of her progress.

I notice most of us (probably without even thinking) are pluralising OP's singular concern when we repeat the word in our own text. I think that's a fairly marginal distinction with concern (both versions sound natural enough to me, and don't really convey any difference in nuance).

But with fears (which I think is idiomatically more likely after allayed) I have the definite sense that the singular form implies one very specific and significant fear. It doesn't seem right to me except in contexts where that specific fear is (or shortly will be) explicitly defined.

I think you're looking for dispell.