I use this format
POST /messaging/v1/messageDefinitionSends/key:External_Key/send
Where External_Key is the one from Your triggered send.
Then, I'm using a sendable Data Extension. If You try to search it with the data related the request, mostly creating a filter, You can find the request.
That doesn't mean the email was sent. You have two methods to get t know what happened:
1) Create a filter and try a preview from the email used to sent this email. Go to the Content folder where your emails are stored. Then you can see some errors there, in case any. You need to preview using the Data Extension (recommended to get a Filtered one)
2) Check the Tracking->Sends->Triggered Sends->Your TS. Then click over the total amount sent. Then try to search the email You used for the test. If NOT found then means the email is not sent and the best approach is to do a preview to see what the error is. The preview you can use the Classic Content or the Content Builder.
Also you can use the endpoint deliveryRecords and get the send status for your request. You will need the response from your request and create a new request to a new endpoint. Get further reference here https://developer.salesforce.com/docs/atlas.en-us.mc-apis.meta/mc-apis/messageDefinitionSendsDeliveryRecords.htm
I highly recommend you to get the postman project for interact with the REST API https://github.com/salesforce-marketingcloud/postman