It's more of an opinion. Today I received an intravenous injection in the emergency room...

This is not an adverse reaction, but the pharmacokinetics of the drug. It occurs most often when the drug is administered too quickly, although it also happens with correct administration and results from sudden, transient vasodilation caused by:

-high levels of sodium phosphate in the dexamethasone solution,

-change in pH and osmolality in venous vessels,

-irritating effects of excipients (e.g. sodium sulphite).

The perineal area has a very rich innervation and a dense network of vessels — hence the burning sensation appears there the fastest.

This burning sensation is not dangerous and usually disappears quickly, but it can be very unpleasant. In clinical practice, there is even talk of "burning crotch syndrome" after dexamethasone — although this is an unofficial term in my community, i.e. paramedics and anesthesiologists.