IAM policy only allowed from Cloudshell?

Recommended not to use 'UserAgent'.

This key should be used carefully. Since the aws:UserAgent value is provided by the caller in an HTTP header, 
unauthorized parties can use modified or custom browsers to provide any aws:UserAgent value that they 
choose. As a result, aws:UserAgent should not be used to prevent unauthorized parties from making 
direct AWS requests. You can use it to allow only specific client applications, and only after 
testing your policy.

I don't know of a way to restrict API calls to CloudShell environments.

You can find examples of IAM policies for CloudShell in this article Here is some basic example:

{
    "Version": "2012-10-17",
    "Statement": [{
        "Sid": "CloudShellUser",
        "Effect": "Allow",
        "Action": [
            "cloudshell:*"
        ],
        "Resource": "*"
    }]
}