No untoward side-effects of phase 1-2 trials of COVID-19 vaccine have been reported (1-2).
Headache, injection-site pain, myalgia, and mild fever could develop in certain people (3) but this could be expected with any intramuscular injection.
According to CDC, there is no definite association of autism and vaccination (4)
1. Article Safety and immunogenicity of the ChAdOx1 nCoV-19 vaccine aga...
I would think of the previous types of vaccines. I might think of some flu-like symptoms, but in a minor form. Unfortunately, we do not have enough information about this vaccine. Therefore, we must be very careful when setting expectations, and stay calm until this vaccine is provided to many people and for a period of no less than a year.