Do these two sentences mean the same?

I'm just feeling so much.
I'm experiencing intense emotions.

Question

Do these two sentences mean the same?

I'm just feeling so much.
I'm experiencing intense emotions.

Answer

They are very similar. The second one is just a bit more precise. Sometimes I use the second one to give the other person a more clear idea of what I'm feeling, especially if they are not an emotionally intense person.

Answer

As Collin says, they're similar.  The first is more informal, and sounds like 'spoken' English.
The second is more precise and academic, written English.

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