To elaborate: Someone who isn't easily affected by their own emotional distress Someone who's tough and doesn't make their own problems into everyone else's problem.
It is unclear whether you want a verb or a noun, perhaps the latter.
A stoic is given by the Oxford Dictionary as
NOUN — A person who can endure pain or hardship without showing their feelings or complaining.
With an example
If you are on one end of the bell curve and need minimal drugs to treat your pain, you're a stoic, a good chap.
The Cambridge Dictionary has the slightly different
adjective — determined not to complain or show your feelings, especially when something bad happens to you.
With an example
We knew she must be in pain, despite her stoic attitude.
I presume you're looking for an adjective. Depending on context, you might use "stoical", "phlegmatic" or "impassive". A stoical kind of person tends to endure pain or hardship better than others. Phlegmatic implies an unemotional and calm response to external stimuli. Impassive is more related to facial expression.
stoical - "seemingly indifferent to or unaffected by pleasure or pain; impassive": "stoic resignation in the face of hunger" TFD , showing austere indifference to joy, grief, pleasure, or pain; calm and unflinching under suffering, bad fortune, etc. Collins
phlegmatic - "having or showing a slow and stolid temperament" MW , "someone who is phlegmatic stays calm even when upsetting or exciting things happen" Collins e.g. He was a most phlegmatic man, steadily working on as the rain splashed down.
impassive - "If someone is impassive or their face is impassive, they are not showing any emotion" e.g. "He searched Hill's impassive face for some indication that he understood.", "The lawyer looked impassively at him and said nothing." Collins