I would ignore it unless it happens again, or you get error messages. you can run a Memtest that would take all night but that would rule out any memory tests, under the search bar type Windows Memory Diagnostic. Run it, when the computer boots change the test settings to extended, and 4 passes.
Also the beeping did it sound like a windows sound, or like a hardware beep, did it come from your speakers, or from inside the laptop? That will make a difference where this will go. But from the sound of things if you shutdown the computer it stops, does the beeping come back? It could have been a fluke, a button got stuck or something letting it sit with out any power may have fixed it.
I'd advise against taking it to a shop right now, that gets very expensive and the problem could be anything, from bad memory, hard drive errors, all which are easily fixable by you. Or it just could have happened once.