I visited a barber and had my hair cut this morning.

I visited a barber and had my hair cut this morning.

And then I went to my university.

But I have had a beastly headache since then.

It hurts.

It prohibited the progress of my work.

So today, I'm going to retire to rest early.

Have a good night's sleep.

• I visited a barber and had my hair cut this morning.
• I visited a barber and had my hair cut this morning, and then I went to my university.

  I've combined this sentence with the next to make the sentences flow more naturally. When you have short sentences, try to see if you can combine them into a compound sentence, unless you want short sentences for dramatic effect. :)

• And then I went to my university.
• And then I went to my university.

• But I have had a beastly headache since then.
• But I have had a beastly headache since then.

  The word "but" is used to introduce a new thing(s) that are contrasting (very different) to what has already been mentioned, so it is not needed here, because we are not contrasting the big headache with anything. We can just introduce the new information like the way that the sentence is corrected up there. :)

• It hurts.
• It hurts.

  Even though this is very short and you can combine it with the previous sentence like "I have had a beastly headache since then, and it hurts", you can leave it like this- really short and abrupt for dramatic effect. :)

• It prohibited the progress of my work.
• This sentence is perfect! No correction needed!

• So today, I'm going to retire to rest early.
• So today, I'm going to retire early to rest early.

  I think that this is more natural, because the way you used "retire" here is to withdraw from working, and you did that early today. :)

• Have a good night's sleep.
• Have a good night's sleep.

  (๑•̀ㅂ•́)و✧

• Have a good night's sleep.
• Have a good night.

  I'm not sure if you're wishing others goodnight but I assume it is.

I think Yansenさん gave great comments about the nuances and usage of words.

I hope you feel better soon! Have a great night, Kanotownさん!