We agree that these larvae, in context with the damage you describe, are probably those of Allium Leafminer. You may need to discard any affected plants if the larva-infested portion can't be cut off after harvest, but otherwise you won't necessarily need to destroy the whole crop if not all plants are affected. Since this insect has a summer dormant period of sorts before the second generation emerges, you have the opportunity to try to prevent egg-laying on the plants at that point (if you replanted later this year) by covering the crop with row cover or insect mesh netting. While there is a risk of trapping adult flies under the cover if they are still present in the soil and emerge after the cover goes over the new plants, you could reduce that risk by either moving the new planting to a new bed location or tilling the soil while the bed is fallow to help expose pupae to predators or to kill any that might remain in that soil between crops.

Miri

Hi, 

These do look like allium leafminer. You can review our information page on them to learn techniques for prevention, but unfortunately if they are already infested, you may need to cut your losses and start again. The best way for prevention is to use row covers in the fall and spring before the flies can get to them. 

If you can harvest the scapes at least, that may be an option if the bulbs are not ready for harvest or are too far gone.

Here is also a helpful YouTube video on them: 

Let us know if you have further questions. 
Emily