Will my arthritis medication (s) interact with other medications?

Yes. Medications for pain and arthritis can interact with many other drugs. This is why your doctor needs to know all the medications you take.
Drug interactions. Without knowing the medications, it is very difficult to say that the medications interact. Your pharmacist should be able to tell you if there is an interaction. If you have an iphone there is an app called epocrates that has a drug interaction check which is what I use in the clinic. With any medications, there is always a chance of drug interactions.