I'm a property crimes detective and deal with this alot, so here it goes, but my answers are based on California Law:
You can always file a police report and they will investigate it as best as they can. The only thing that matters after all this time is whether or not the stolen items can actually be located.
There are databases that some pawn shops and agencies share that keep records of pawn sales. Not all agencies or shops participate, though. It usually depends on whether or not there is an ordinance that requires it if a pawn shop wants to conduct business within a certain jurisdiction.
California law requires that pawn shops keep transaction records. Most require only a name, thumbprint, and description of jewelry, but how accurate the description is depends on the shop. Some will copy the driver license, some will photograph the jewelry, but many simply offer only a vague description, which makes it nearly impossible. If you have a picture of the item, then by all means, provide it to the Police.
But, the Police will have a better chance tracking a name rather than the item itself. Providing the name of your friend will give the Police a good lead. They can call pawn shops and ask if a certain person has sold anything there and by law, they have to be truthful. Unfortunately, some aren't, though. If she is on probation (with a search clause), the Police can search her residence, vehicle, etc, to see if she still has it in her possession.
In California, a pawn shop is required to hold the item sold for 30 days before selling it. If it has been only two weeks, there is a good chance that it is still sitting in the safe at the pawn shop. Gold sales are way up because of the value of gold now, but there are many mail-in businesses that don't ask any questions.
In California, if your item is found at a pawn shop, then the Police can put a hold on it, but they cannot return it to you right away. Although the item belongs to you and the shop now cannot sell it legally, there are civil laws that protect the pawn shop because they have a financial interest in the disposition of the ring, unless there is evidence that shows that the pawn shop knew the item was stolen at the time of purchase. If a suspect is convicted, then the court can order the suspect to reimburse the shop and order the items returned to the owner. Or, the pawn shop can agree to return it to you and only seek resistution from the suspect.
So, let's say the Police find your jewelry at a pawn shop and there is evidence that your friend is the one that sold it, as a detective, this is what I would be asking the District Attorney to consider:
1) Theft (of the jewelry from your home. The severity, i.e. felony or misdemeanor, would depend on the value of it).
2) Possession of stolen property (because your friend clearly was in possession of your stolen item at the pawn shop)
3) Theft (at the pawn shop, because your friend received money based on the sale of stolen property. It is a fraudulent transaction. The severity would depend on how much she received for the item).
3) Burglary (at the pawn shop, because your friend went into the shop with the intent to commit a theft).
You could certainly request that the Police "drop charges," but your involvement basically ends at your front door. It may not protect your friend from what she did at the pawn shop.
Good luck to you. I hope you get your things back!