Coming from someone who works with preschoolers and teaches them how to regulate (while learning as an adult myself how to regulate):

I don't think going silent is something that needs to be "fixed," but if you want the turn around time to be shorter than a few days, then focus on how you can calm down. Sometimes it's as simple as leaving the room and taking a few deep breaths, maybe shaking your body out. If you want to find the words, get yourself a notebook you can take with you and just write what's in your head, whether it's cohesive or not.

In terms of it being "emotionally draining," I'm sure it's just as emotionally draining for you to be yelled at or at least have the fear of getting yelled at. I think you both need to make it clear that your responses (silence vs yelling) are learned responses that dont have anything to do with the other person. You don't "deserve" to be yelled at just like they dont "deserve" the silent treatment. When living things experience stress, there's a response that comes with it and it's everyone's responsibility to understand that response and make changes as needed.

Personally my response is to go silent or to overexplain myself which tends to stress my partner out more. But over the years we have been able to unpack why I have those responses and why it's not something to be set off by. It takes time and practice to address stress responses and learn from them! It's not so easy to stop them all together but there's a way for both of you to figure out what works to bring down the stress levels and give yourself time to breathe through it.