Here is a long article on both Chlorella and Spirulina I just found. The main cautionary takeaways from it appear to be that consumers need to be sure these products are tested for purity by a reliable independent company, that there are many claims made for these products, but these claims have never been verified in any credible scientific study, they may produce side effects in some people, and it may be best to take these substances for only a limited length of time. On the other hand, they are great sources of certain nutrients. I'm not sure what to make of all this, but I'm going to continue taking Chlorella for now, but as @gardeningjunkie mentioned, Chlorella pills can be HUGE as is the case with the one I am taking now, so I need to find another brand.
https://www.livestrong.com/article/494368-the-harmful-effects-of-chlorella-spirulina/