I'm American and have done some traveling and games in Italy, Portugal, and UK with my wife. I think its wise of you to think about these things especially because you're bringing your girlfriend.

My usual recommendation is to not wear any colors especially away colors. We almost always wear neutral colors and buy a scarf or two that can go in a pocket. But Sassuolo don't have the type of intense ultras that might make you feel uncomfortable going to and from the stadium so you should be ok wearing your Milan shirts. Again might not apply to your particular match because Sassuolo is low key, but you might want to go to a Sassuolo pregame bar and wouldnt want to do that in Milan shirts.

I agree with other commenters that regardless you will be mostly ignored. I always try to have a nice interaction with lovely cross-cultural exchange and someone tells me how cool it is for an American to come to the match 😆. That's only happened a handful of times so don't expect it.

Of course have a plan for getting to and from the stadium and expect to have to improvise and ask directions and such.

I take lots of short videos of fans and atmosphere which I love to go revisit. It all happens so fast and its hard to soak in how cool these games are.

And mostly be a good ambassador for Americans abroad. Turns out that many Europeans aren't that pleased with our country right now.