Re: different medications
It depends on what the Antibiotic is and also the type of Anti-inflammatory you decide you take. In addition, I would need to know which pain killer you are taking for your cold symptoms.
Certain NSAIDs (non-steroidal anti-inflammatories) should not or is not recommended to be taking with a few selective antibiotics. Will need specific names of the medications.
And as far as my concern with the other current pain killer for cold symptom combined with potentially a new pain killer if needed is the potential for the combined doses on both of them to be at an additive level, leading to a greater dosage than what it recommended; there's always a certain up limit dose per any medication. So again, need specific names of medications.
Plus, are you taking any other medications (i.e. oral contraceptives, anti-diabetic, blood pressure medication, etc, etc, etc). Always concerned about drug interactions. Sometimes doctors may not be aware of what other medications the patient may be taking.