Google Fi will give you a new sim for free, quickly shipped free to your USA address. Either port in your old number or get a new one for free. Once activated while in the USA, you can pause it at any time. The plan is $20 per month, when not using data. With pausing and resuming you only pay for the hours you have it unpaused. That is 2.8 cents per hour, or 67 cents per day. Pay $0 per month for times you do not use it, though google will unpause automatically every 90 days. This is what I use when in USA, and all other international travel days outside Argentina. Once settled in Argentina I pause except for the day/hour I need some SMS from someone who cannot send to a VOIP.
If you need a USA number to make daily cell phone calls or data from your cell phone during your life in Argentina, then this plan is not price efficient. But for the issue you describe, it is more than ideal.
You do not need to use your cell phone to sms message or pause or unpause. Do from your computer.
https://messages.google.com/web/conversations
https://support.google.com/fi/answer/6188337?hl=en