This is excellent! I have a few corrections:

First day of work (after the holidays)

Today I was all day trying to work all day. [<em>In English, the phrase "was trying to work" should stay together, and "all day" comes at the end. You can also put "all day" in the beginning of the sentence, as in "All day today, I was trying to work."</em>].

I woke up at eight o'clock and, in this at that moment, a friend phoned me to talk about how horrible was his first day of work was after the holidays...One hour later, he finished the conversation and I could have breakfast with my flatmate (we were talking about work again).

Then I opened my computer and tried to do some work. I organized all my tasks, wrote some emails and answered questions about the courses I organize [teach? I am not sure what you want to say here]. But it was like if I couldn't do it in a good way and the time was slowest every hour. [<em>I am not sure what this sentence means.</em>] Finally, I let ended my tasks and went to shop at downtown.

Tomorrow I woke up will wake up earlier and I hope to do my work best best work. ["Will wake up" is the correct future tense.]

Nice job! ¡Buena suerte mañana!