How to overcome Semi hourly limit?


I am developing a system to alert the Malaysian citizens about the haze situation in the country usually caused by fires from the country itself or neighboring countries.
I am updating the data every 6 hours in separate tweets which sums up to about 60 every 6 hours. I was not aware that the daily limit of 2400 per day was (please correct me if I am wrong) divided into semi hourly quota; meaning about 50 for every 30 minutes.
Now my system which is in testing stage cannot update tweets anymore, is there a way to overcome these two issues?:

  1. Send 50-100 message every 6 hours.
  2. Get my system to be able to send updates again.

or, did I breach any terms of use?