As Macmillan explains, when you use "feel" with a bare infinitive ("She feels some ghastly Fright come up"), it typically means:
to notice something that is touching you or something that is happening to your body
When you use it with an ordinary finite clause ("She feels (that) some ghastly Fright comes up"), though, "feel" typically means one of two things:
- To have a particular way of thinking about something, especially one that depends on your emotions rather than on facts or evidence
- to notice something that you know is there but cannot see, hear, touch, or smell
Of course, the bare infinitive is always "come," whereas the finite simple present would here be the third-person singular "comes."
So replacing "come" with "comes" would result in the word "feel" having a somewhat different meaning. In particular, one would likely interpret "feel" in your version as "believes," whereas "feel" in Dickinson's version means something more like "viscerally experiences."
As a further example, compare:
- I felt he was trying to grab me.
- I felt him try to grab me.
Only (2) entails that he actually touched you.