Your doctor seems to have done everything right, which, sadly, isn't always the case, so s/he is definitely worth keeping.
Side-effects are not all down to the direct effects of the med. Psychology can be at least a big as important a factor. Believe you are going to suffer greatly and an anxious mind is quite capable of producing the whole catastrophe for you.
Despite the impression given by Dr Google, and even support forums like this one, most taking antidepressants for the first time don't experience severe side-effects. But if you do, keep reminding yourself that a) side-effects are rarely signs of physical harm, and b) in most cases the end result is usually worth the initial problems.
You seem to be doing all the right things so have an excellent chance of getting your life back onto an even keel.