As has already been mentioned, you can in fact restart from the last level played since the game saves your progress. However, here are some things you should know to help you get through those last few levels:
- Starting at stage 17, you'll find that the power pellets either do nothing at all, or only work for a few tenths of a second, max. They will usually make the ghosts change their pattern which helps.
- At around stage 19-20, the ghosts speed up to the point that they can catch up to you during straightaways, even if you've already cleared the dots. You can still get away from them by making a lot of quick cornering.
- You'll need to learn to master the fake-out around stage 19-20 as well; if you quickly change directions a couple of times, the ghosts will usually change their patterns, and allow you to make near-miss escapes.
- I would suggest using the D-pad instead of the stick for the higher levels; it seemed to me that around stage 17-18, the input from the thumbsticks isn't fast enough to be precise - you'll miss turns, go the wrong way, etc. If you have one of the new transforming D-pads (I didn't) it may help even more.
Good luck!