Overall, you should be able to switch from Paxil to Zoloft without significant issues. However, some people are VERY sensitive to the differences in the medications, and it can cause some side effects such as you are experiencing.
I did a quick Google search for "switching from Paxil to Zoloft" and there are a number of message boards that discuss this - in most cases people don't have a problem, but if they do, it can be alleviated by reducing the dose of Paxil & then ramping up the Zoloft, or just waiting it out (lasts a couple of weeks it appears).
As for the drugs being safe & non-addicting, almost all antidepressant or anti anxiety medications will have physical withdrawal symptoms. This is because they actually change your brain chemistry to control the levels of chemicals that alter our mood or pain perception (called neurotransmitters, examples are dopamine, norepinephrine & serotonin). In most cases, they are -not- addictive in the way street drugs are - you don't need to take them & do so in increasing doses to get the same effects.
So, part of what you are experiencing is likely due to the differences in the chemical make-up of the drug (they are not exactly the same, but very similar & it is common to switch from one to the other), and part of it is probably because your body is very responsive, & thus sensitive, to the changes.
Just as a personal example - I took Cymbalta for a number of years when it was first approved for Fibromyalgia. However, I didn't really need an antidepressant & it didn't offer the pain-relief benefits I needed. I quit "cold turkey" when I forgot to get it refilled. Had mild dizziness for about 2 days & then I was fine. My pharmacist weaned off it when she got pregnant, & it took her over 2 weeks - she had to open the smallest dose capsules & take a portion of the drug powder, and had moderate to severe reactions when she tried to back off the drug too quickly. Same drug, different effects.
Regarding their safety - most drug testing is done on the general population. They are not usually tested on small children, or pregnant women, due to the greater likelihood of adverse effects, some of which can be severe or damaging. Prozac & Zoloft are 2 antidepressants which have been given a FDA grade C - meaning that they have not been proven to harm fetuses. Paxil is graded D - it HAS shown adverse affects on unborn babies, and should not be taken while pregnant.
Since you weren't pregnant or trying to conceive when the Paxil was prescribed, chances are the more appropriate drug was given to you, but under these new circumstances, allowances need to be made to protect the baby. It sounds like your doctor & pharmacist have given you the correct information, I hope some of this extra info was helpful as well.
Try to stay calm, and perhaps contact your doctor/pharmacist to see if tapering your doses @ this point might be helpful, or if there is anything you can take to offset the side effects you are experiencing. Best to you & the little one yet to come! T.