"Presented today with" vs "presented herself today with"?

It is common in medicine, either in practice or in medical literature, to talk of a patient presenting (intransitive).
For example: "The patient presented with interstitial oedematous pancreatitis."

To present: To appear for examination or treatment, said of a patient.
[Farlex Partner Medical Dictionary]

A letter of referral from the diagnosing doctor to the hospital doctors would therefore normally say "She presented today with symptoms of COPD". The inclusion of "herself" is redundant in this usage.

The full context of the letter is not clear from your question but I assume it to be from a diagnosing doctor (either in the hospital or in general practice) to a hospital doctor. In either case "to the hospital" or "at the hospital" is not needed because the context is entirely clear. Nor is the phrase needed as a qualifier to "she presented".