One grammatical errors, I noticed.
+Remove the quotes contained in the brackets below:
"I was wondering if you could find out all the details about the island and the hospital["], ["]I also wanted to know if my brother is alright. The whole place is really shady, and they haven't let me see my own brother".
Now with the story, I found it very enjoyable. One thing I did have trouble believing was the main character openly admitting that he was a private investigator. I think maybe him making up an excuse and getting denied would have been more of better approach. It's almost as if an undercover cop admits who he is to someone he is investigating. This is just an opinion of mine, you don't have to cater to it.
Also, I did feel as if you could have continued with it. The ending seemed more like a pause or a breather moment for this part, not really closure. It would be nice if maybe you continued with him trying to find the whereabouts of the brother for his client. This could lead to him learning more of what other kinds of experiments are being conducted, maybe even leading him to being captured himself, and inevitably thrown into a state of madness to where they want to conduct these tests on him. We might even see the results of said tests through his eyes.
I'm not trying to write your story for you, but you can see how there are various ways it can be expanded upon more. Nonetheless, I do like your story and felt it was written fairly well. I hope to read more of your works.