Note that I'm in the UK, so the examples I use may seem odd to other standards. The principles however should be the same.
There's restrictions at several levels that need to be looked at here - the first is how much current the cable from the socket can safely carry in its state. In this case it clearly wasn't anywhere near good enough, perhaps it would've still packed up if it was uncoiled, we can't know without knowing details of the cable. All of the extension leads I make have cable rated at 16A or above - yes it's a bit overkill when I can only draw 13A max from a single socket, but I require them occasionally when 16A plugs and supplies are in use. That way I can simply change the plug at the end without worrying about whether the cable will melt if someone draws a bit too much current through it!
As long as you're well within all these limits (and any others that might exist, I'm not saying that's an exhaustive list!) then you're fine. So if your upstairs ring main has a limit of 32A and you're drawing 25A worth of stuff, you'd need to run it from 2 different plug sockets that weren't part of the same double socket, but you could still use the same ring main quite safely. If you had 35A worth of stuff for whatever reason, it's a different story and yes you would need to start running cables all over the house!
Beyond this, there's the limit of each socket (13A max), the limit of each double socket (usually around 20A between the two sockets - people tend to forget this but very few double sockets are rated to supply 13A to each socket at once!) the limit on your ring main (often 16A or 32A) and finally the limit of the total current coming into the house. If you blow that last one then you're doing something seriously seriously wrong!
Yes, in some cases you'll know when you've overrated something. If you draw more than 13A from a socket, the fuse should blow. If you draw more than 32A from a 32A ring main, the MCB on the ring main should trip. But it's very bad practice to rely on these instead of doing your own calculations - they should be seen as precautionary measures only in case you screw up. Also, some weaknesses in the chain (such as the 20A limit from a double plug socket and the above under-rated cable configuration) won't be protected in any way at all, and could cause serious damage, start a fire, or worse kill someone.
I know that sounds melodramatic, but electricity can be lethal even on a domestic level if people mess around with it. I for one would always advise that when you're not sure over something, check it with the relevant calculations, double check, and if you're still not sure get someone who is! This isn't meant as a go at anyone, I'm genuinally glad no-one was hurt and that you learnt your lesson
I just hope this goes down as a reminder to everyone that reads it!