Exercise increases your immune system in the long run, but exercising while sick can lead to increased length of recovery. See below:

Rest or exercise when sick?
Fitness enthusiasts are often uncertain of whether they
should exercise or rest during sickness. Human studies
are lacking to provide definitive answers. Animal
studies, however, generally support the finding that one
or two periods of exhaustive exercise following
injection of the animal with certain types of viruses or
bacteria lead to a more frequent appearance of infection
and more severe symptoms (Davis et al., 1997; Gross
et al., 1998).
With athletes, it is well established that the ability to
compete is reduced during sickness (Friman and Ilback,
1998). Also, several case histories have shown that
sudden and unexplained downturns in athletic
performance can sometimes be traced to a recent bout
of sickness. In some athletes, exercising when sick can
lead to a severely debilitating state known as “post-
viral fatigue syndrome” (Maffulli et al., 1993; Parker
et al., 1996). The symptoms can persist for several
months, and include weakness, inability to train hard,
easy fatigability, frequent infections, and depression.
Concerning exercising when sick, most clinical
authorities in the area of exercise immunology
recommend (Friman and Ilback, 1998; Mackinnon,
1999):
• If one has common cold symptoms (e.g., runny
nose and sore throat without fever or general body
aches and pains), intensive exercise training may
be safely resumed a few days after the resolution of
symptoms.
• Mild-to-moderate exercise (e.g., walking) when sick
with the common cold does not appear to be harmful.
In two studies using nasal sprays of a rhinovirus
leading to common cold symptoms, subjects were
able to engage in exercise during the course of the
illness without any negative effects on severity of
symptoms or performance capability (Weidner et al.,
1997, 1998).
• With symptoms of fever, extreme tiredness, muscle
aches, and swollen lymph glands, 2-4 weeks should
probably be allowed before resumption of intensive
training