No. The definition of addictive means that once you start taking it, you need more and more to get the same effect. WB, and none of the ssri's, are addictive. You CAN have something called discontinuation syndrome, which happens if you try to stop taking them too quickly, and even if you do wean off, some people, (me included) still have ds. BUT, it should not deter you from taking the meds, if you really need them. You will be going on them with support, and going off them with support, too, and that can make ds much easier.
Some of the things you MAY experience in ds are nausea, headache, dizziness, and something called "brain zaps". These are not scary. They are just little "blips" like feeling like your brain takes a second to catch up to your head... but they go away in a couple of days, and like I said, if you know they could be coming, you get through them really fine.
They may not even happen to you. Most people do not get any symptoms of ds when they wean off these drugs.
Are you seeing a pdoc? or is this your GP? You should always get meds through a pdoc, or be seeing one for med mgmt. while you are taking them.
But no, they are not addictive. You should see a therapist and a specialist in psychiatric meds, though, and NOT just a gp or OB.