Cheech,
It is still winter in NorCal. The rain on ~ the 9th kicked the NFAR flow up to 10,000 cfs though it is now down to a little less the 2000 cfs however one should not even try to swim in it at 250 cfs as you can not get back up river as the flow is strong. As it has already been said the rocks are slippery. Even moderate water flows at this time of year are Cold making falling into the water and incurring an injury could be a near death experience. Even the places you've had suggested to go to may not have many people there and then they will be busy with what they are doing, the only person looking out for you will be you. Being out there with a healing body part is only adding to the potential danger to yourself.
As has been said the water in CA is low however we could still get snow into May and any "Winter" storm can turn deadly, be prepared to take care of yourself for at least a week if you are snowed in.
The Auburn area is a great place to be, the prospecting shop there will welcome you and likely will be able to supply you with helpful info. Understand that the Auburn area is part of the 1849 gold rush so lots of history and possibilities abound. I would suggest you wait till summer like early June especially if any additional snow and rain develop as the water will be much lower, safer and more places will be accessible for camping as well as prospecting. There are many trails out of the Auburn area, again the prospecting shop in Auburn can help you with info. on them. if you are physically in good shape and bring along a pack you could even backpack down some gentler trails to a river/creek and campout. Check out my thread "A picture is worth a thousand words, approximately..........63bkpkr" in the journals section at the top of the prospecting info and you will see pictures of what the river looks like during the 'summer' months. Some of the trails down to the NFAR require serious physical fitness as well as a hiking staff AND the bears are plentiful and will rob your food bag unless you are very good at hanging it. They know enough to chew through a rope.
Best of luck with your trip....................63bkpkr