they may cause some mild side effects in a small number of children (not many) but that is still far more preferable to actually getting (and spreading) those awful diseases.
This is not true, reactions can be horrible though shortlived illnesses and some reactions can be life changing and severe hence even the government have a vaccine damage fund.
This type of rhetoric is not truthful and the full truth should be given to allow all parents to agree to vaccination.
This constant barrage of basically saying "stop being silly, just do it" puts off a lot of parents who would otherwise vaccinate as like the op says the Dr fobbed her off.
My Dr fobbed me off so I read about it decided vaccination was overall good but that I didn't fully agree with the ages it was given so varied the schedule. Something that after speaking to other doctors about, quite a few doctors vary the schedule for their own dc.
Remember that vaccinations are for the greater good and the schedule is as much about large scale financial efficiency as much as it is about efficacy..
So find a doctor that discusses things with you properly. The reaction may be something that you do need to worry about so discuss with a sensible helpful doctor. It is likely nothing to worry about but your concerns should not just be quickly dismissed out of hand.