Can Oxycontin and oxycodone-acedaminaphen be taken at the same time?

That is a question you need to ask your doctor or pharmacist.

It doesn't make sense for your doctor to prescribe 2 different brands of the same medication expecting you to take them both.

Most likely your doctor messed up - but maybe not, the pharmacist should have alerted you.

Call your pharmacy or doctor right away to find out.