It's understandable to be worried. I had some trepidation about requiring a tetanus booster at 39 weeks pregnant with DS (thanks cat) so discussed the pros and cons with my doctor before having it done. I also had the WC booster about 2 weeks after giving birth, neither caused any problems for either myself or DS
The Boostrix is Whooping cough, Tetanus and Dipheria all in 1 injection.

It is routine to offer in hospital to all mums after giving birth nowadays. And a large % take up the offer with no side effects.