I'm on t3.medium and cpu is to slow, so switched to t3.xlarge so it is much better, but the cost is double

Yes, you have a few options to optimize your costs while still meeting your performance needs:

1. Instance Scheduling: You can indeed set up automation to switch between instance types at different times of day. For example, you could use a t3.medium at night when demand is lower, and switch to a t3.xlarge during the day when you need more performance. This can be accomplished using AWS Lambda functions triggered by CloudWatch Events/EventBridge rules.

2. Reserved Instances (RIs) or Savings Plans: To save costs on long-term commitments, you can purchase Reserved Instances or Savings Plans for 1 or 3 year terms. By paying upfront (either partially or fully), you can achieve significant discounts compared to on-demand pricing. This is especially beneficial if you have predictable usage patterns.

3. Compute Savings Plans: These are more flexible than RIs and apply to EC2 instances regardless of instance family, size, AZ, region, or OS. They still offer substantial savings over on-demand pricing.

4. Consider other instance types: Depending on your workload, you might find better price-performance ratios with other instance families. For example, some of the AMD-based instances (like t3a) or ARM-based instances (like t4g) might offer better value for your specific use case.

Remember to carefully analyze your workload patterns and requirements before committing to long-term savings options. Also, ensure that any instance type changes (whether manual or automated) don't disrupt your applications or services.

Sources
can we buy compute savings plans for difference of amount | AWS re:Post
EC2 instance type | AWS re:Post
Compatibility and Potential Issues when Changing EC2 Instance Type from t3.xlarge to t3a.2xlarge | AWS re:Post