sentir vs sentirse
Sentir is feeling or sensing something external. Sentirse is how you feel inside — your personal emotional state.
sentir
To feel or sense something — an external thing, a sensation, or to feel sorry about something.
Siento frío.
I feel cold.
A physical sensation you're registering. Not your inner state — the cold is external.
Lo siento mucho.
I'm so sorry.
'Lo siento' = I'm sorry. Fixed phrase. Sentirse lo would be wrong.
Siento que algo va mal.
I sense something's wrong.
An intuition or feeling about something outside yourself.
sentirse
To feel (reflexive) — your internal emotional or physical state.
Me siento fatal hoy.
I feel terrible today.
Your internal state — how you are. Siento fatal would mean you sense something terrible.
Se siente sola.
She feels lonely.
Emotional state — it belongs to her inner world.
¿Cómo te sientes?
How are you feeling?
The standard way to ask about someone's wellbeing. ¿Cómo sientes? would be asking what they're sensing — odd.
Tricky bit
'Siento frío' (I feel cold — external sensation) vs 'me siento bien' (I feel well — internal state). The reflexive signals the feeling is about yourself. Mix them up and you change what the feeling is about.