I looked up the definition of pity (Oxford English dictionary):

the feeling of sorrow and compassion caused by the sufferings and misfortunes of others.
"her voice was full of pity"

synonyms: compassion, commiseration, condolence, sorrow, regret, sadness, distress, sympathy, fellow feeling, understanding, feeling, emotion;

I think that maybe we use the word 'pity' more to imply a level of superior condescension: 'I pity you', but that doesn't seem to be the dictionary definition.

Sympathy definition:
'feelings of pity and sorrow for someone else's misfortune.'

Empathy definition:
'the ability to understand and share the feelings of another.'

I want/need to be comforted - verbally hugged, or if she offered something non-verbal I'd go for that. Sympathy feels more comforting than empathy, or is being comforted something different altogether?