Hi ElizabethS! All gyms in Buenos Aires city are required by law to ask you to submit a doctor's note saying you are fit to work out, and the note is valid for one year. All big gyms are going to ask you for one, but maybe if you try a small "barrio" one they'll be more linient. In all public pools you are also required to undergo a quick medical checkup which is done by the physician working there, they check you for fungi, cavities and lice, and this is also done regularly (approx once a month).
Also, most big gyms have annual memberships and if you're only staying for one month they are going to charge you more. It seems like a lot of hassle for just one month, so I'd suggest you try a small gym near where you'll be living, or just working out in a public park (good weather is coming now).
If you want to go to a fancy gym anyway, you can (i) ask if they have a physician on site (big gyms offer that service for a small fee and you can get checked rigth there) or (ii) if you have health insurance, go see any general practitioner (medico clinico), but if the doc doesn't have your medical records, he'll probably ask you to have a routine lab test (blood and urine) and maybe something else before issuing the certificate. So, in-house gym doctor is probably much faster (at Megatlon they take your BP and make you take an EKG, but it's all done there at the doctor's office inside the gym).
Hope this helps! Good luck!