Good luck!

Margaret doesn't go to the library immediately. Nor does she start in on diagram recharging. Before she does any more runecasting, she's going to get a better understanding of her dragon powers. She makes a largeish light+control diagram, puts a rock on it, and incants, "Cause this rock to glow red for three seconds, and then to glow red for three seconds every time the person touching it does any magic other than by saying an incantation and using a diagram."

The rock glows red for three seconds, flickers, and then resumes glowing red. It continues to do this with the every three second flicker as long as Margaret's touching it.

Maybe using her medallion to pass for human counts as using magic, rather than the medallion doing magic to her. Maybe touching the detection rock counts as using magic. She can test the first one by going fullform in her bedroom and taking her medallion off for a minute.

The rock quits glowing when she does this.

At least it isn't recursive. Still, dragon fullform is not the most convenient for doing science. She disenchants the rock and tries again: "Cause this rock to glow red for three seconds, and then to glow red for three seconds every time the person touching it does any magic other than by saying an incantation and using a diagram or by using a medallion."

The rock glows red for three seconds and then stops.

And if she enchants a different rock to glow and then disenchants it, that doesn't set the detector off either, right?

It does not.

Okay. Now for the important test: what if she repeats one of the failed incantations from her experiments with light colors, one that did nothing but used up the diagram?

Three seconds of red.

Yup, she's definitely been using dragon magic to avoid dying of science. But now at least she can tell when something will be safe for her to teach other people. If medallions ends up blocked on her needing to recruit a member of some obscure species, maybe she can pick up the bags of holding project again. 

Just for completeness, she repeats an experiment that did nothing and didn't expend the diagram.

She is not doing any hidden magic then.

Okay, so that's probably just the thing she says not counting as an incantation, or something.

Now she can try recharging diagrams! The diagram she uses for disenchanting already has a reasonable set of rune meanings, conveniently. Her first incantation attempt is "Recharge the diagram on top of this one, make it usable again." 

Nope.

How about a new digram, with meanings light, control, and reverse, and the incantation for making a rock glow with "and also recharge this diagram so it can be used again" tacked on the end?

Nope!

She's not sure how much clearer she can make these incantations. And those red pulses of light from her magic-detecting rock are a bit unnerving in their implications. Hmm, what if she does a normal ordinary "make a rock glow" spell while trying to do unspecified dragon magic at it?

The new rock does not glow.

Wow, she was not expecting that to work without a more precisely specified intention. So dragon magic does or at least defaults to a fairly narrow thing, and that thing is magic suppression, and it can suppress the effects of messing up a spell without her deliberately trying to, which is extremely fortunate. 

Hmmm, what if she it again and consciously only tries to suppress the fact of the diagram being expended, while permitting the actual effect?

That doesn't work; depending on exactly how she concentrates on it she can get the spell to go off, or the diagram to be unexpended, but not both.

Yeah, that was a long shot. At least it's cool that she can fail both of the plausible ways rather than getting the same result every time.

She visits the Avalon library again, looking for anything on species-specific natural magic, especially healing.

Some people say angels can do that. It's also a reputed ability of sphinxes.

Figures that it would be a probably-extinct species and a very hard to find one. Not to mention that a member of either species might turn out to be hostile to her for inscrutable reasons. She texts Bella:

I looked up creatures with natural healing. Bad news: it's sphinxes and angels. I don't suppose you've made any sphinx or angel friends on your travels?

I can't say that I have. You're going to have to redesign the spell anyway to compensate for not knowing all the Arabic, right?