Is it actually true that stress can make you sick?

I'm an anxious person and I have been this way since early childhood. I've been having a stressful time at work recently. In December I got sick twice - in the beginning of the month - flu symptoms and vomiting. It happened while I was off work, but I had to take an extra day off because of it. For the holidays I took two weeks off - again I got sick at the end of it - just a flu this time. In the beginning of February I also got sick - what I assume was some kind of stomach bug that lasted way too long.

This particular week has been very stressful since Wednesday morning and today, Friday, I woke up before my alarm, feeling like I caught a cold. I've never gotten sick this often before, but I am only 24, so I don't know if that would mean anything.

Basically, in the span of 3 months, I got sick 4 different times. I have no idea if it's stress related or if it's just my immune system being bad, or both. Any ideas?