While you can technically use both erected and installed, you should stick with built as it is far, far more common and easily understood.
'Super dams' should be built for the growing sea level.
Erected is on a huge downward usage trend, and it's usually used in very specific applications. These typically refer to processes that are literally bottom up, but also somewhat trivial to complete. You might hear that "the construction workers erected additional scaffolding", but that's about it.
The word installed could work, but only in the most abstract sense. Typically, installation refers to placing something prefabricated (like a refrigerator or new windows) in a spot made for it. Not a brand new building or structure.
English doesn't require you to be ultra-formal, even in a professional setting. If you were to try to avoid saying build and built in an engineering document or context, people would think you're intentionally trying to sound superior -- not that you're being professional. Err on the side of simplicity and being common unless you're explicitly told otherwise.