How doable would my trip itinerary be without the Yellow Fever vaccine?

In late April to early May, I’m gonna take my first trip down through some countries in Latin America. I’m an avid traveler who mainly goes to the big cities, but I haven’t been to Latin America yet, just Europe, North Africa, some Middle East, and East Asia. I’ve never had to really prepare and get vaccinations (other than covid stuff) to go abroad.

I’m gonna be going, in this order, to Mexico (CDMX), Panama (Panama City layover, will leave the airport), Brazil (Rio), Argentina (Buenos Aires), Uruguay (Montevideo day trip/overnight), Ecuador (Guayaquil, layover and will leave the airport), and Colombia (Bogota, staying in the airport) before I go back to the U.S. With this trip I had totally forgotten about the possible need for the Yellow Fever vaccination and any possible restrictions that countries will impose. Especially when I did a little research yesterday, there tends to be restrictions for many countries if you’re coming in from Brazil.

I don’t even have that yellow vaccination book and I messaged my doctor’s office about how to go about getting the Yellow Fever vaccine, may be calling them tomorrow on Monday. In case I don’t get it by my trip, is my trip even possible or will I get denied entry into Argentina and/or Uruguay and Ecuador due to recently being in Brazil with no vaccination at the time?