durchmachen
to go through
To experience and get through a difficult, exhausting, or unpleasant phase or situation.
Nach ihrer Krankheit hat sie eine schwere Zeit durchgemacht.
After her illness, she went through a difficult time.

to go through / stay up
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to go through
To experience and get through a difficult, exhausting, or unpleasant phase or situation.
Nach ihrer Krankheit hat sie eine schwere Zeit durchgemacht.
After her illness, she went through a difficult time.

'Durchmachen' (to go through/stay up) is a separable verb. The prefix 'durch-' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er macht gerade eine schwere Phase durch.
He is going through a difficult phase right now.
The prefix 'durch-' emphasizes that you experience a process or period of time from beginning to end. This applies to all meanings: a difficult time, an entire night, or an illness.
Wir haben die Nacht durchgemacht und den Sonnenaufgang gesehen.
We stayed up through the night and saw the sunrise.
In this meaning, 'durchmachen' (to go through) is often combined with negative or difficult phases of life. Typical objects are 'eine schwere Zeit' (a difficult time), 'eine Krise' (a crisis), or 'eine Trennung' (a breakup/separation).
Meine Freundin hat letztes Jahr eine schlimme Trennung durchgemacht.
My friend went through a terrible breakup last year.
You can often recognize this meaning by the fact that a time expression like 'die Nacht' (the night) is used as the object. Sometimes the verb also appears without an object if it is clear from context that it is about staying awake.
Vor der wichtigen Präsentation habe ich die ganze Nacht durchgemacht.
Before the important presentation, I stayed up all night.
This meaning is used almost exclusively for typical childhood illnesses that one has once in life. Common examples are 'die Windpocken' (chickenpox), 'die Masern' (measles), or 'Mumps' (mumps).
Als Kind habe ich die Masern durchgemacht und war zwei Wochen im Bett.
As a child, I went through measles and was in bed for two weeks.
to learn / experience
'erfahren' and 'durchmachen' can both describe someone experiencing a situation. 'erfahren' is more general and can also refer to individual experiences, feelings, or states. 'durchmachen' emphasizes more strongly that a phase is difficult, exhausting, or unpleasant, and that you experience it all the way through. It often fits crises, illnesses, or long-lasting problems. If you only want to say that someone experienced something, 'erfahren' fits. If you want to show that it was a stressful time, 'durchmachen' is more natural.

Meine Nachbarin macht gerade eine schwere Zeit durch.
My neighbor is going through a difficult time right now.
Johanna erfährt im neuen Verein viel Freundlichkeit.
Johanna experiences a lot of kindness in the new club.