Yes your battery may be the culprit, but it sounds more like your alternator
is dead or dying.  You managed to drive it initially because the person you
bought the vehicle from had completely charged the battery before you got
it.  As you drove it it wasn't getting charged by the alternator and finally
drained down to the point that your car wouldn't start or run at all.  After
a jump from your friend gave you enough juice to drive for a little while,
the same thing happened again (and again).

It doesn't sound like you're in the US, but I'm sure you most likely have an
auto parts store or repair shop that can test your battery and alternator
for you (usually for free), but from what you write I'm almost certain that
it's your alternator.  Now the issue is to replace it quick enough before it
also completely kills your battery and you have to replace that as well.

Cheers - Jonathan

1.Get a Heavy Discharge Test done on the battery, most garages/electrics
services can do this instantly.
2.Get alternator output checked
3.Replace 1.and or 2.