EDIT: Wow what would you know. OP went to the hospital and they said it is fine. Literally just an allergy. The "ER Doctor" was completely 100% wrong.

You're an ER Doctor? Why would you even try to diagnose somebody off of a single picture? Going as far as telling them to start taking meds for your magical ability to diagnose somebody by looking at a red line on their arm.

As a "doctor" you should KNOW how dangerous it is to misdiagnose someone. You should ALSO know that a diagnosis of Thrombophlebitis needs testing first before a diagnosis.

Your advice for OP also looks kiiiinda suspiciously exactly like the treatment recommendations from fucking googling Thrombophlebitis. "General self-care, warm compress, Nonsteroidal anti-inflammatory drug (NSAID)."

If you were a doctor you would know on top of that, that Thrombophlebitis doesn't cause solid red lines going perpendicular to the veins in someone's arm. It comes with bruising in the general area much like taking a heavy impact.