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Serendipitous. Adjective.

I got in a horrible car accident and broke my leg, but falling in love with my nurse at the hospital was serendipitous

Wiktionary says:

combination of events which are not individually beneficial, but
occurring together to produce a good or wonderful outcome.

The idea behind serendipity (its noun form) is that a beneficial outcome emerges from one or more chance events. Your example speaker didn't choose to get in an accident, but that accident led to falling in love. Another example: a romantic comedy like Pretty Woman may have plenty of misfortune but it has a serendipitous outcome: two people fall in love.

One phrase associated with serendipity that seems especially applicable to your example is "happy accident," one translation of felix culpa.

noun: blessing in disguise

an apparent misfortune that eventually has good results

On the Bright Side would work here:

used to refer to the good part of something that is mostly bad

In your sentence:

"I got in a horrible car accident and broke my leg, but on the bright side, I ended up falling in love with my nurse at the hospital."

A term for the situation is an ill wind.

That's short for the proverb ‘It's an ill wind that blows nobody any good.’  Wiktionary paraphrases that as:

An action or occurrence must be very bad indeed if it brings no benefit to anyone.

According to The Phrase Finder, this is a many-centuries-old sailing metaphor, meaning that:

a wind that was unlucky for one person would bring good fortune to another.

The term is often used when mentioning the good outcome, as in these examples from The Free Dictionary:

The rain caused flooding, but it may help the farmers.  It's an ill wind, as they say.

The fire destroyed half the village.  For the builders business has never been better.  It’s an ill wind…

And Collins:

But it's an ill wind; I recovered and married one of my nurses from that hospital.

Consolation is almost exactly that. OED:

"the comfort received by a person after a loss or disappointment

• 
  there was consolation in knowing that others were worse off"

So, to use the original example: ""I got in a horrible car accident and broke my leg, but falling in love with my nurse at the hospital was a consolation".

Although, compensation might work better in that example.

The word irony has undergone a bit of a semantic shift and is often used for a perceived contradiction, among others a contradiction between one's expectations and an actual fact or event.

Merriam-Webster gives as one of its meanings

incongruity between the actual result of a sequence of events and the normal or expected result

and continues with examples in which the outcome is worse than expected; but it can be used for better outcomes as well, like in your case:

"Falling in love with the nurse was the irony of my accident." Or "ironically, getting fired was the best thing that had happened to me in a long time".