You can (and should) set up an AWS CloudWatch alert on your account that will send you an email or SMS notification when your monthly bill exceeds a set threshold.
There are a couple of things that are easy to overlook when using billing metrics.
1. All billing metrics are stored in us-east-1 even for usages in other regions.
2. If you are using consolidated billing, billing metrics will be published under the linked account, and will only be visible to that account.
Hope that helps.
...what? Is this true? If so, can someone explain the logic behind this?