Shingles would be due to the immune system being depleted (a lot of things can trigger re-activation of that), it doesn't have to be from the shot per se, but because the immune system has gone hay wire... which is a reaction one can have to any vaccine on the market (not just Coronavirus).

Get them to have Vitamin B (liquid over tablets if able) or if able, Vitamin B shots. It will support the blood-cell creation process and help them recover faster.