In general viruses "break in" to cells in order to use their replication machinery to
make more viruses. In the case of SARS-CoV-2 the spike protein is the part of
the virus that is used to "break in". It's not dangerous in itself, it's part
of the toolkit this virus uses to gain control of cells and make more viruses.

In order for the human immune system to fight against a foreign chemical or
"antigen" (usually a protein of some kind since living things use proteins as
building blocks) it needs to be exposed to the antigen and build antibodies
(and other immune responses). Many of the vaccines use methods of delivering
or generating the spike protein in order to "teach" the immune system what to
be alert to. Some use "killed" viruses instead, but none of these are in use
in the USA and Europe to my knowledge.

So, vaccines are not inherently damaging, as you state. They cause your 
immune system to react, which is the point, and this can result in soreness
at the injection site, fevers, aches, and similar symptoms. Yes, anaphylactic
shock can result from an allergic reaction to the vaccine itself - as it can
from peanuts, eggs, insect bites or seafood for example. In the UK, as I said in the show, we
are asked to wait for 15 minutes after our vaccination in case such an
allergic reaction is triggered, and there are medics nearby to deal with any
such emergencies.