Acceptable substitute for oyster sauce?

The perfect solution - if you can tolerate bonito (fish) - is to take a teaspoon or two (depending on the degree of fishy taste you want) of dashi, which are granules made from bonito fish and kelp, dissolve them in 2 tablespoons soy sauce, a tablespoon and a half of brown sugar, two tablespoons of potato (or corn) starch until they are all dissolved into a paste. Next, chop up four cleaned and washed medium sized shiitake mushrooms with the end of the stems cut off and discarded, and boil them in two cups of spring water until the water gets brown from the mushrooms. Combine the dashi mixture and stir until it thickens, then boil for a couple of minutes until it is the consistency you would like (syrupy and thick is best for most recipes). Pour mixture to a cool dish and cover for at least one hour (two or three is better) and then use in place of oyster sauce. This is so delicious that I even substitute oyster broth for water to make my own. Commercial oyster sauce is nowhere near as tasty!
Enjoy!

I get a vegetarian oyster sauce, made with mushrooms.
You want a deep umami flavor--soy or tamari are part of that, maybe try some mushroom stock base (Better than Bullion has one) added in. Perhaps Black Bean sauce would work, just know that some are spiked with chili or garlic and that becomes the predominant flavor. Miso also has some of the flavors you are looking for.
Hoisin is too sweet and Worchestershire too acidic. Fish sauce Dan also be sharp, but a bit mixed in adds a depth of flavor.

Question: my daughter is allergic to wheat dairy eggs and walnuts. We want to fix lo mein for her but both soy sauce and oyster have wheat in them what is best to use. Ill try and find the The vegetarian oyster sauce

Oyster sauce is thick, which fish sauce is not. And Worcestershire is too piquant. Maybe a more reasonable facsimile would be to mix a bit of hoisin and dark soy sauce, since the soy would temper hoisin's sweetness but also impart umami while not compromising its thickness too much. Though it really depends on what you're trying to cook (stir-fried vegetable vs braise).

I do not think there are oysters in oyster sauce. Worcestershire sauce is a good substitute, but try reading the list of ingredients on the oyster sauce bottle.

Are you allergic to fish? If not, you could try subbing fish sauce if you're sure it's not contaminated with oysters.