Tantrums are a common behaviour of children suffering from anxiety disorders (and OCD is one of the anxiety disorders). The usual treatment for anxiety disorders is intervention, therapy and possibly medication. It sounds as if your child psychiatrist has experience in this area. By the way, our child was placed on Prozac for a few months at six years of age (severe social anxiey disorder) and it did wonders. Today, she is taking a newer SSRI medication (Celexa) at a low dosage and probably will be taking meds for her entire life but the alternative was not an option. Without this medication, our child had no life. Your words "her tantrums have been unbearable" - if living with your daughter is unabearable, I wonder what it would be like for your daughter to live this way. One more thing - if the medication does not work, then it can be stopped.
As for the autism - can't offer any advice or experience there. I wish you the best ...
There are lots of people totally against medication, especially for children because their brain is developing and there is no way of knowing how it could affect her long term. There are some permanent side effects to some medications that are given for these types of problems. However, there are also parents who have to use medication because that is the only thing that helps.
All I would say is that it sounds like you are just at the beginning of what most families would say is a lifelong journey. There is an awful lot you can find out about your daughter and how she is affected by autism and OCD (if it is indeed OCD on top of autism, and not just rigid repeitive behaviours, or a need for rituals or routines which are commonly part of the behaviours under the umbrella of autism).
So I would also encourage you to read up about autism in general, and also specifically how it affects your daughter.
Can you give an example of the OCD behaviour you see her displaying?