Not really. What you have is an autoimmune illness where your antibodies are attacking you instead of bacteria/ viral invaders. Because you are "ill" at some level all the time, you are more susceptible to catching other peoples illness.
The "immune suppressed" bit comes into play when you take medications that suppress your antibodies, so they will stop attacking you. Biologics are this kind of medication. They make your antibodies less reactive, so your body takes less damage, but then they are also much less reactive when you get new bacterial/ viral infections from external sources, like family or friends...
As for your second question, your immune system is not necessarily "over-active" as much as it is confused, thinking that your body parts are invaders that need to be attacked. But yes, your autoimmune system is active when it has no reason to be. If you take a Biologic, then your immune system is decidedly under-active. Several researchers think that the autoimmune system gets "sensitized " by a previous infection (mono, etc.), and then never gets the signal to quit, and so it attacks your body instead...