Hello Faith (@collielady), welcome to Connect. You've come to the right place to ask questions and find out what others have done for treatment of similar health issues. I'm not familiar with followup testing after surgery for lung carcinoids but thought I would jump in until others with better information can join in and offer what they know. The American Cancer Society has a little information that may be helpful here:
https://www.cancer.org/cancer/lung-carcinoid-tumor/after-treatment/follow-up.html
Did your doctor team or surgeons discuss any follow up treatments with you that you can share?

Also, I would like to share one of my favorite tools for finding information including recent articles, testing, treatments on pretty much anything. Google Scholar (https://scholar.google.com/) is a great place to do your own research. It really helps to be your own advocate - and that's what you are doing here on Connect. Here's an example - I did a search on Google Scholar using your phrase "follow up testing after surgery for lung carcinoids" and it returned the following results. I also clicked on 2017 at the left to get the most recent results.
https://scholar.google.com/scholar?as_ylo=2017&q=follow+up+testing+after+surgery+for+lung+carcinoids&hl=en&as_sdt=0,24
Keep asking questions and learn as much as you can about your health concern! You really are your best advocate.

John