Hmm I think this sentence should be checked by a native...

NNC English

Does the Spanish make sense?

hmm more or less, I don't see the relation between the two parts of the sentence but both make sense on their own, the Spanish sentence says something like "yesterday I went to the doctor, and I wrote the essay myself."

Would be better if it was: "Yesterday I went to the doctor and when I came back I wrote essay myself"?

The problem is that I'm not sure that the Spanish is natural, at least not without some context. Maybe the sentences should just be deleted ?

,and I wrote the essay myself.

OK, I'm changing this to "Yesterday I went to the doctor and when I came back I wrote the essay myself." - that is internally logic. It doesn't have any context, but I don't think it is needed. Basically, almost every sentence needs a context. Besides, the sentence itself is making some... hmmm... "time schedule" context - at least that's how I see it.

A comma after "doctor" and a comma after "back" would make this easier to read.

I still think that commas would make this easier to read, but it's not wrong, so I'll remove the "@needs native check" tag and add an OK tag.