You are wise to be careful about this. Finding a competent bike shop can be tricky in some parts of the country. I had this same problem recently and am waiting to see what kind of job a local bike shop does on my Zipp wheel. Something about racing on a poorly laced wheel that strikes me as perfidious.

-Robert

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"How wonderful it is that nobody need wait a single moment before starting to improve the world." ~Anne Frank

It would be prudent to check other nipples before hand (cracks /corrosion / rounded off) and also the wheels spoke tension..

In theory you would be fine to simply replace the single spoke nipple... get a few spares though.. in case you have another go and also in case you butcher one installing etc..
Re getting the correct one, simply remove an adjacent one and match it.. likely a 12 or 14mm square drive if traditional.. whether or not it has thread lock or propriety thread lock depends on your wheel brand.. either way a standard spoke with thread lock will do the same job..

Also ask why it failed.. materials issue/ Install issue? of course hard to tell.. a lower tension wheel causing variation in spoke load causing fatigue and failure.. possibly.. corrosion due to sweat and insufficient maintenance .. possible..

If a short time after you have repaired this spoke a number more fail, then yes replace all and rebuild the wheel.. re-use spokes if the wheel is not old, if it has 15,000kms - 20,000kms (3yrs plus for example) plus on it then prudent to rebuild with new spokes... (at this point you would also consider if worthwhile to replace wheels with new and retire the old etc..)

Best of luck

Broken spoke nipples (especially aluminum nipples) are a tell-tale sign that spoke length is too short.

Have many miles on it?
Ridden in wet weather? Corrosion?
Where was it built?

If one nipple broke the odds of more breaking could be fairly high. But yes, you can just replace it and true the wheel. It's probably a standard 2.0mm (14ga) nipple which any bike shop would have.

? IME rare for that to be the primary cause in factory built, or even a reputable hand built wheels ..

Some nipples appear under inserted but the threaded section is typically central (off set toward the head rather than the neck), as long as all the threads are engaged by the spoke then any beyond that are there only to support variation.... having 2-3 threads showing above the nipple head is also common...

Normally Fatigue (mechanical cyclic .. accelarated by insufficient / imbalanced spoke tension or simply cycle count ie use / age..), Fatigue (corrosion usually anodic), and then of course incorrect spec / build... which you mention...

Actually, with factory built wheels it's not an uncommon thing. Spokes that are properly tensioned and the proper length will have the spoke end at or just a little beyond the nipple driver slot. Chronic nipple breakage is usually one of two things: either galvanic corrosion (aluminum) or the spoke length is two short. This assumes that the nipple flats haven't been compromised (rounded off) by an ill fitting spoke wrench.

Spokes that are overly stressed usually break at the j-bend.

I dont know the age or who built the wheel.

I did snap my chain during a hill sprint about a month ago, I dont think it hit the wheel but I was more worried about not flipping over the front than anything else, when I stopped my chain was laying on the ground.

Have any of you built a wheel using your bike as the truing stand? I ask because if I buy one and all the tools to build this wheel it will cost the same as buying another used PT wheel so I am trying to decide what direction to go.

Absolutely you can use the frAme as a wheel building jig..
A little more faff but not much.
Go on line and look up how to build / true a wheel..
A basic knowledge patience and common sense will get you there..
Once you have the tools doin a quick wheel check each month keeps the wheels running true..
Dive in it's pretty much the only last rewarding bit of bike maintenance..
Best of luck..