Do cats get flu? -and sneeze and cough..?

Our cat is the next addition to the family, and we love him dearly. But he's the first cat I've ever owned and I feel a bit out of my depth, for the past few days he's been feeling very sick and weak, and even disappeared for a day or 2 over the weekend, it started off with him sneezing, and now he is actually coughing, sneezing, and doing a bit of a wheeze type thing- almost like he's got the biggest fur ball ever lodged in his throat, but its lasted quite a while now... What do I do? I'm so worried about him, he's acting and looking just like a human when they get bad flu.. Do I take him to the vet or are there things I can do for him at home? Thank you!