If your update is once every 10 minutes it will be less then 20 mb per month..
You can check logs to see the raw messages from your device. If you want to be more accurate you can have script to calculate all real messages. Alternatively you can check average message size and multiply by the total number of messages.
Also you need to add a bit of buffer of top for the network protocol headers etc.
How can I check how much data has been transferred to the server on a given day? I don't have the ability to monitor data usage on my SIM card.