How to make nostrils bigger after alar base reduction?

Yes, strictly said alar wedge reductions are irreversible, that is whey they have to be handled with great caution, accurately planned and meticulously performed.
With that said, you have to distinguish between:
-removing the scars: unfeasible, not even hiding them; in the best case they can be revised
-restore the tissue lost if your nostrils are pinched, too narrow or the alae are flad without their natural curvature outwards; this is somehow feasible with a composite graft; the donor side might be varied, this should be examined and analyzed, however there would be a "segment" effect, with two scars; other option are the nasolabial flaps to make a better quality of the reconstruction
Anyhow I'd be happy to assess your case you seek expert opinion about revisions.
If you wish better grounded opinion please do post or send privately well lit, focused and standard images: frontal, both lateral and both oblique views, also underneath the nostrils.
Feel free to request any additional information from me.

Dear straightbridge in Reston, VA:
I am sorry that you are not happy with the alar base reduction.  It is difficult to make the nostrils wider without possibly grafting some tissue and that would involve some highly visible incisions and, generally, this is not done.  Whether or not making the bridge more narrow would make your nose even tinier is hard to answer because without photos.  I am sorry your scars are noticeable when you make a face.  External incisions have some potential for being visible regardless of the skill of the surgeon.  My best advice, be conservative. 

Best wishes,

Robert Kotler, MD, FACS 

Revision rhinoplasty might be able to widen alar base in some patients. However, revision rhinoplasty is not reversing the previous alar base reduction or nostril narrowing. If you haven't already, then speak with a rhinoplasty specialist to review options.
Best,
Dr. Chaboki