The other day, I had my 2002 Sienna Symphony towed (first time ever

) I went and got it back today and verified that it had no physical damage and no personal property had been taken.
It had already been positioned for us to just jump in and drive straight out. It got driven about 45 miles today from the tow lot to my home with no problems.
When I got home we went to back it into a spot and it began making some awful noises. They sounded somewhere between loud exhaust noise and a really, really loud rattle - neither of which was something it was doing before the tow.
We were able to replicate the noise with the car both in reverse and in park by turning the wheel in certain directions. Looking under the car while it was rattling, it seems to be coming from the undercarriage, near the rear wheels but somewhat in front of them.
There did not seem to be any issues starting the car or driving it forward that we noticed. Unfortunately we NEED to use the car for a fairly long trip this weekend (apx 300 miles total) to move an elderly parent.
Looking online a wide variety of things get mentioned as possible culprits, including a heat shield, a U Joint and the transmission. I have had one car with transmission issues in the past (99 Ford Taurus wagon) and my Sienna is not behaving ANYTHING like that car did when the transmission went.
Anyone have any insight as to what this may be? I am a girl with almost no car knowledge and I would like to sound like I at least know a little of what I'm talking about when I go to the repair shop on Monday!
EDIT: I should probably add this. It has about 118,000 miles on it. The last time I drove it before Friday afternoon was Sunday night. I have no idea what method they used to tow it.