I'll add to this that there are lots of colors of noise: white, pink, brown, etc... OP and anyone else looking for a solution should try a wide range of colored noise to see what works best for them (if any)... I personally like something closer to brown, as true white noise is too high-pitched / staticky for me...

FWIW I use a LectroFan machine set on "Chestnut"... And it also has fan sounds too... Here's a pic from their website, with the 20 different settings (10 fan & 10 white-to-brown noise)

https://www.soundofsleep.com/wp-content/uploads/2016/08/B00E6D6LQY.PT04.jpg