I need three credits to graduate. Is there a reputable independent study or online program that can let me do this in under a month?
You should check with your school to see who they will take credits from first. The University of Phoenix and other for-profits offer accelerated classes (around 5 weeks), not sure who else does.
To do something in under a month would be really, really hard - though having said that, there are summer courses that can sometimes be completed on-site in three weeks, so maybe on-line isn’t that far-fetched. Check with your state’s community college system to see what they have available. They often have accelerated summer courses, so your odds of finding something that brief and on-line are probably better than elsewhere. Beyond that, you know for sure it’s accredited.