I would recommend one of the SSRI meds, like Zoloft, Celexa, Lexapro,
Prozac, etc. Those are MUCH more appropriate meds to treat anxiety issues versus the SNRIs like Effexor.
Do not stop taking it on your own. You will need to be gradually tapered off. You've only been on it a month, so you shouldn't need too long to taper. Effexor is notoriously one of the harder ADs to come off of, which is why you want to do this correctly.
Definitely talk to your doc.