Sim card and your own us plan

You can switch back and forth on your phone. Ask your US carrier to convert your physical SIM into an eSIM and use the slot for the Italian SIM. If you have two slots, ignore that and just pop the second SIM in.

If your phone has just one SIM slot, then you take out the US SIM card (put it in a very safe place for keeping) and put the international SIM into your phone. This renders the US SIM card inoperational - it can't get calls or text and can't be charged for any usage, apart from your normal monthly bill. The international SIM will have its own telephone number, different than your US number.

It has 2 sim slots.

I'm afraid I'm not familiar (yet) with phones with 2 SIM slots, nor with a combination eSIM and physical SIM. I hope to get there with my next phone!

I have an iPhone XS, which is a few years old. It has 2 SIMs, one real and the other an eSIM.

Here in the US, I have 2 cell phone lines, my personal cell which is keyed into my eSIM, and my business cell is set up for the real, hard copy SIM.

When I travel abroad, I take out the hard copy SIM and replace it with a European SIM. I tell my phone to use the foreign SIM to be the provider of cellular data so it is part of my European plan. It has a European phone number, but my eSIM still has my personal cell phone number. Friends and family can call me on the personal cell number, and when I am in Europe, I use the other phone line to make calls abroad.

Anyone calling me on my business cell probably gets a message that I can't answer, or maybe something else. I don't know. Maybe it goes to message, but I can't confirm that.

Assuming you have 2 SIM slots, use one for your regular line and the other for the European SIM; you're just adding an extension to your phone. You can call out on either number, although the American number will be much more expensive to use from Europe.

The thing is, I don't want phone calls or texts coming from the US on my US sim because of the cost. I wondered if there is some setting you could switch over, so no calls come and when I reach the US I could switch it back. Of course I could just take it out.

Can you put a second SIM card in your phone to try out how two SIMs work in your phone before you go? If it works like phones with a physical SIM and an eSIM, you should be able in the Settings menu to turn one SIM off even though it is still in the phone. Of course, you can always just remove the physical SIM that is for your U.S. number.

You can switch your US SIM off--on an iPhone, at least, it's easy to toggle between phone lines. Settings--->Cellular--->Cellular plans

I don't have an Android phone and have never used one, but I can't imagine that it would be much different.

The thing is, I don't want phone calls or texts coming from the US on my US sim because of the cost.

Not sure as to others experience, but check with your carrier, but the plans I had, you do not incur costs receiving calls or texts, even in Europe, and those making the call or text do not incur international fees. However, if you call the US, you do incur the cost of an international call.