For individual swim meets you can see the results posted (at the meet) or online afterwards. But they only give you a snapshot of your progress between two specific swims.
The best way to get a long-term picture of your progress (hopefully improvement) over time is to use Take Your Marks. Although it is not free (currently costs $30/year for a family of up to 3 swimmers), it can be a helpful way to see your progress. They also offer a free trial if you want to check it out before paying anything.
Result for Swimming New Zealand meet are posted to the database, so your times are already available for you.