Sharon - what may be an 'everyday noise during the day, may well be an antisocial noise at night - when there is less general, background noise, so any sound sounds louder, and when most people are trying to sleep.
For example - it is not generally antisocial to hoover or play music or let your children run round (or to indulge in many other noisy activities) during the day, but they become antisocial at night - because of the sound carrying further and sounding louder when it is generally much quieter, and because people are trying to sleep.
And no-one can say that the OP's breast pump is not noisy, and cannot be waking the neighbour up - because they are not there! Maybe the OP's pump is running louder than the norm, maybe it's the vibrations and they way they are being transmitted through the floor or walls that's to blame, maybe the sound insulation between the flats is particularly poor, or maybe the neighbour is a very light sleeper - or maybe it's a combination of all the above.
Think on this - if the pump is not waking the neighbour up at 3am each night, what is? The OP says it can't be her alarm, and if she was thundering noisily round the flat each time she gets up to pump, surely the neighbour would have complained about being woken by her loud footsteps at 3am, not the sound of the pump?
The neighbour clearly is being woken at 3am each night. If she was sleeping through it, she wouldn't be aware of what the OP was doing each night, and would therefore not know there was anything to complain about.
Waking your neighbour in the middle of the night, every night is anti-social - as the OP seems to have accepted - and I hope the steps she's going to take will sort the problem out.