AWS Lambda function unable to establish connection to SQL Server RDS instance - sql-server

Question

I have written the following small Lambda function in .NET core for testing purposes. It is triggered on a PUT in an S3 bucket, and should show the object name in CloudWatch and insert the object name into a table in an RDS instance.
Here is the code:
public async Task<string> FunctionHandler(S3Event evnt, ILambdaContext context)
{
context.Logger.LogLine("context.Logger.LogLine function begin");
var s3Event = evnt.Records?[0].S3;
if(s3Event == null)
{
context.Logger.LogLine("No S3 Events recorded");
return null;
}
try
{
var response = await this.S3Client.GetObjectMetadataAsync(s3Event.Bucket.Name, s3Event.Object.Key);
context.Logger.LogLine("S3 Key: " + s3Event.Object.Key.ToString());
var connectionString = Environment.GetEnvironmentVariable("ConnectionString");
SqlConnection c = new SqlConnection(connectionString);
c.Open();
SqlCommand cmd = new SqlCommand("INSERT INTO LambdaTestTable (ValueText) VALUES('" + s3Event.Object.Key + "')", c);
cmd.ExecuteNonQuery();
c.Close();
return response.Headers.ContentType;
}
catch(Exception e)
{
context.Logger.LogLine($"Error getting object {s3Event.Object.Key} from bucket {s3Event.Bucket.Name}. Make sure they exist and your bucket is in the same region as this function.");
context.Logger.LogLine(e.Message);
context.Logger.LogLine(e.StackTrace);
throw;
}
}
I get the following output in CloudWatch:
START RequestId: 15c5eddb-8171-11e7-af34-251688cfddb2 Version: $LATEST
Console.WriteLine function begin context.Logger.LogLine function begin
S3 Key: TaskTemplate.dp Error found Error getting object
TaskTemplate.dp from bucket api-dev-dpstorage-s3. Make sure they exist
and your bucket is in the same region as this function. A
network-related or instance-specific error occurred while establishing
a connection to SQL Server. The server was not found or was not
accessible. Verify that the instance name is correct and that SQL
Server is configured to allow remote connections. (provider: TCP
Provider, error: 40 - Could not open a connection to SQL Server)
Two errors I am unclear on here. Firstly, while CloudWatch successfully shows my object key once the file is PUT to the bucket, it then has an error saying it can't find the object? Secondly, it has a network / instance error trying to connect to the SQL RDS instance. I am using a connection string which is used successfully within an EC2 instance by another application.