She has been feeling much better since she left the hospital last week.
This is the good construction of the sentence, present perfect continuous. However, I thought you couldn't use a specific time expression with the present perfect tenses.
I would have said "She is feeling much better since she left the hospital last week." as we can use the continuous tense to talk about an extended period of time.
You probably don't want to use the present perfect to describe an event that happened at a specific time. For example, this would be wrong:
She has felt better when she left the hospital last week.
However, in your sentence the "feeling" does not happen at a specific time; it has been happening continuously since an event last week. Here is another example of a similar usage:
I have visited Chicago three times since 2005.
Even though a specific time is mentioned, that is not the time of the "visiting". Therefore, the present perfect is fine.
Also, note that the present perfect is used for action that began earlier and continues into the present time. It is therefore appropriate for your sentence for that reason, too.
The rule about present perfect is that you cannot use finished time expressions.
In your sample sentence, the time expression that modifies the present perfect is "since she left the hospital last week". A time expression with "since" indicates the time something began, not a finished time, and I believe they always require perfect tenses.
The "since"-expression refers to a finished time, but only to indicate when the period of time began, not to indicate when she felt better. Her feeling better started when she left hospital, but it continued at least until the time this sentence was produced.
The simple answer is that "since last week" is not a specific time.
A specific time would be a sentence like "she has been feeling much better at 2pm", and is not recommended because the present perfect, being a mash-up of present tense and perfect aspect, involves two times - the time of some past event, and its continuing relevance in the present. As present perfect needs two times involved, tying it all to one specific time such as 2pm cannot work.
However, tying down the time of only the past event by saying something like "since last week" doesn't cause any conflict as we still have two times. The event last week, and the present relevance.
She was feeling much better and she is still feeling much better so the correct tense is present perfect continuous.When we talk about something which started in the past and is still ongoing we use present perfect tenses.
