Unfortunately, the only thing you can do about this is to email support@airtable.com and ask them to reset your automation runs for the remainder of the month.
Also, as you mentioned, upgrading to Enterprise is another option to increase your automation runs, but the Enterprise Sales Team is not very responsive so that could take weeks or months.
Note that your invoice billing period probably doesn't occur on the first of the month, which is likely why the automation runs weren't reset on the first. Everybody is on a different billing cycle, which is based on when you started paying for Airtable.
It's definitely a shame that Airtable doesn't give its customers any way to pay for more automation runs, because once you've hit the limit, your entire company could come to a screeching halt.
For a better long-term solution, this is one of the Top 20 Reasons why I highly recommend that people outsource as many of their Airtable automations as possible to Make's Airtable automations & integrations.
Not only are Make's automations & integrations significantly more powerful & customizable than Airtable's native automations, but Make always lets you buy more automation runs if you ever run out, and you can even set it to automatically purchase more runs on your behalf. If you need any technical help with Make (or Airtable), I am available for hire as an expert Airtable consultant to help.