Store bought sperm count tests

My husband and I have been together for almost 9 years. We split up for a while because we disagreed on certain things we wanted in life but since have worked them out and I'm so blessed we did.
We TTC for 2 years as well before we split which I think played a minor role in our attitudes toward each other. 
While we were split, I had a one night stand (not proud of it at all but I was honest with him and he did the same.) well, I got pregnant. And now we are on our 3rd month TTC again and you all know how emotional this journey is.
He has agreed to do the home test kit. I just don't know how accurate they are.
I also have thyroid issues so I want some answers.
He agreed if there is something wrong we can look into other avenues. He refused the last time we tried so I'm glad he's coming around.

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