I guess there are tests you can do with certain tools. I''m not sure what those would be but I bet a microscope would be one of them. Maybe you could do a search online?
To be certain you will need to have its refractive index and/or specific gravity checked, neither of which can easily be done at home unless you just happen to have a refractometer or some heavy liquids hanging around.
There are some filters called Hanneman Hodgkinson Filters which come in various types and work like a Chelsea Filter - you look through it and certain stones turn different colours. For example with the Chelsea, which you use for green gemstones, a tsavorite will look green, whereas an emerald will glow red - so you could pick a tsavorite out from a bunch of emeralds easily (not that you probably couldn't without!).
It's not quite as simple as that, but that is the gist of it. They have one for aquamarines. I've never had a go with anything other than a chelsea filter so I've no idea if they are any good... apparently you see green through it for an aqua and blue for a blue topaz.
On the inclusion side, aquamarine is pretty clean, and most of it is heat-treated any inclusions that there were will have been altered. Under the microscope you might find straight growth lines or raindrop like inclusions - which you won't in topaz (the most likely stone to find yours is if it isn't an aqua).