If you have a true allergy you would want to avoid all types of onions, garlic, shallots, chives, etc. Onions and garlic are aromatics. You could try some other aromatics such as celery, bell pepper, fennel, etc. They will add flavor and texture to your dishes although you will not get onion or garlic flavor.
If you do not have a true allergy you could try some other things. (Some people don't have a true allergy but suffer from gastrointestinal distress or "tummy trouble" after eating onions or garlic.) If this is the case you could try shallots, chives, garlic chives, scallions, leeks, etc. in small amounts to see if they bother you. Other options that do not tend to cause GI distress when small amounts are used would be dried onions, onion powder, dried garlic, garlic powder, or dried shallots.
Other than this, I would suggest looking for seasoning blends that could add flavors that appeal without containing onion or garlic. You may luck out and find something that satisfies your taste so that you won't miss the onion or garlic flavor. If you do find something, celery could add texture that may be missing.