I was in a similar situation (although instigated by health problems my employer knew nothing about). I was offered another job when I wasn't even looking for one, handed in a week's notice and within half a day of my new job realised I'd made a big mistake, contacted my line manager who wanted to just take me back straight away, but her boss (the director) said no. I didn't tell them about the health problem thing, but I did offer a humble apology and said I'd been a plonker and made a terrible mistake, which my line manager accepted.
So I had to re-apply for my old job, go through the whole interview process and that's how I was reinstated. Which was deeply unfair on the other candidates but I guess I screwed them over by leaving so they screwed me back by putting me though all that? I was probably out of a job for a month or so before I was finally re-employed so that was hard.
My "reliability" was questioned on my next review because I'd left abruptly and it was a bit awkward (and humiliating) for a few weeks/months after and it possibly delayed my future promotions. But after a year or so they pretty much brushed the whole incident under the carpet and it was as if I'd never left.
If you can re-apply for your old job, then do it if you can deal with the crap that may come with it, bearing in mind if they don't think you're reliable enough, no matter how well qualified and competent you were at your job, they may decide not to re-employ you.