Yes getting or being sick during the first trimester during your pregnancy can increase your chances of having a miscarriage.
It's best to try to avoid getting sick however sometimes you still might get sick but it doesn't always mean that you will have a miscarriage even if you do get sick or have the flu or a cold virus during your first trimester.
However studies have shown that having a regular cold, a sinus infection, or even a stomach virus isn't likely to affect your your pregnancy or cause any problems especially once you get past your first trimester during pregnancy.
Still anything can happen and you should have regular checkups during your pregnancy to make sure things are going good.
But most people give birth to a healthy baby even when they've become sick with the flu, cold or other virus during their first trimester.