Yes, you can
The Wild Companion feature you gain at 2nd level says:
You gain the ability to summon a spirit that assumes an animal form: as an action, you can expend a use of your Wild Shape feature to cast the find familiar spell, without material components
The Wild Shape feature (also gained at second level) says:
Starting at 2nd level, you can use your action to magically assume the shape of a beast that you have seen before. You can use this feature twice. You regain expended uses when you finish a short or long rest.
So you have two uses of Wild Shape per short rest. You could spend one of them to summon a familiar and the other one to transform with Wild Shape. There is nothing that states that you cannot use both uses at the same time; only, normally if you use the Wild Shape to transform a second time, you of course lose your original transformation.
The kinds of beasts you can transform into is only limited by CR, and that they originally may not have a fly speed. A crab would qualify.