What is a word that means unforgettable but with a negative connotation?

For some purposes, I like:

indelible: making marks that cannot be removed

It makes me thinks of spills, stains, bad tattoos, burns... things that you want to delete, but can't.

Though I think @Sven-Yargs hit it on the head with haunting.

traumatic may fit, even though the word means basically "causing mental or emotional problems, usually for a long time".

It was a traumatic experience for all of us.

Not all unforgettable events are traumatic but most traumatic events will be unforgettable.

You would be able to get away with seared into my memory or similar variations as a phrase to describe such an event.

The train crash I saw that afternoon was seared into my memory.

The report on teen drug use seared itself into my memory.

I cannot think of any adjectives that would suit your purpose, however.

If you're looking for adjectives, as opposed to phrases, then I think there are three good candidates:

inextirpable: incapable of being destroyed

inexpungible: incapable of being obliterated

inerasable: incapable of being erased

Of course, the implication with these words is that we might, in fact, like to destroy, obliterate, or erase the things they describe. They would be good fits for describing a memory that you would rather not have but can't seem to rid yourself of.