I can understand,if your doctor thought that it was a Superficial Phlebitis
then I would say that the appearance of the skin would be there for some days or may be a couple of week.
I am happy that your are on anti biotics.
There is a mediation very effective in superficial phlebitis called Hirudoid gel apply it on the affected area two times a day and hopefully you ll get better results.
Thanks very much and all the best.