Since you have indulged in an unprotected (assuming so)sexual act just a month before you need to get regular check ups either online or offline after 1 month,3 months, 6 months,1 year.As not all STDs show up immediately. Some pathogens stay dormant for years and then only show up. So it's better to get both you and your partner to be tested.
Regarding the labs you can choose any recognised lab nearby. Not a single test can finalize the results.
Please do consult for further information.
Next Steps
Always practice safe sex. Use condoms.