"Doctor, I have had a very sore throat since yesterday."
Translation:Docteur, j'ai très mal à la gorge depuis hier.
No. In English we have the present perfect tense (have had) for action that started in the past and continues into the present. French lacks this tense. Instead, they use the present tense with the time word depuis to convey the same meaning.
Je mange depuis 15 minutes => I have been eating for 15 minutes.