If someone else's drugs were found in my car after I was arrested for DUI, can I be charged for possession?
What's known as an “inventory search” is what is done to your car after they arrest you, to ensure (supposedly) that nothing is stolen from your car while in storage. This assumes that they had some cause to arrest you before the inventory search. Assuming that they had probable cause to arrest you for driving under the influence, then they could hardly let you drive your car to the police impound lot. But if you had a sober, licensed passenger who could have and was willing to drive your car home, then they should not have seized the car for police storage and therefore no inventory search was needed. Under that circumstance, the results of the search might possibly be excluded from being used against you, which could mean the charges would be dismissed.
There are several other possibilities unstated in your question, and one for example is that during their DWI investigation, they smelled marijuana in your car, or saw white powder on your moustache and in the car’s ashtray. That would create probable cause to search the car even if it didn’t need to be towed or impounded or inventory searched.
The other issue your question raises is whether the drugs can be proved to be yours. That other individuals also operate the car gives credence to your defense, but beware of this, as your testimony that you didn’t know who put the drugs there narrows down the list of who did, and could open up an investigation of who DID put the drugs there.
You need to tell a lawyer the whole story though. There are many other factors not covered by your question. If you had not consumed any alcohol, but had glassy eyes and were driving erratically, this might have supported the knowing possession of the drugs (depending on what drugs they were). A blood test that showed drugs in your bloodstream would help the prosecution considerably. If you took a breath test, you won’t have that problem.