The other day I had my home's water quality tested. I had it done by what seems to be a famous company's environmental analysis center.
Literal
Other-day our-house [gen-の] water-quality check [obj-を] did. A certain famous company [gen-の] environmental-analysis center [or-something-とかいう] place [at-に] do-[have-done-てもらいました].
先日 ('the other day') is a formal/polite time adverb. 我が家 ('our house') is a slightly literary/formal variant of うち. ~とかいう ('something called X, or so they say') is a hedging locution, used when the speaker isn't fully sure of the name or wants to keep some distance. してもらいました is the humble receiving-favor 'I had it done (for me).' The polite register throughout signals a reflective first-person narrative, likely from a blog or letter.