I got infected with an STD from my partner and we both went to the local clinic and got tested. Weeks later it came back, am I still infected?

STD. Both of u were tested. Were both of u treated? Did u both complete treatment? See doc again for culture & sensitivity to make sure std was not resistant to antibiotic. Make sure partner completed treatment as well. No sex until both of u are cured.
Probably. Typically, when an std is diagnosed both you and your partner should be treated and you both should abstain from sexual contact until the treatment is over. If this isn't followed, it is usual for the infection to come back.