I was wrong. The hypothetical form of くれる is くれれば. And you were right the hypothetical form of 来る is 来れば. This does make more sense since 持つ on its own actually just means to hold, not to bring.
Now knowing that, I don’t think there is anything that implies who the subject is since we have no context to go off of.
If it was “I should’ve brought my computer”, I would expect the sentence to be
パソコンを持ってくればよかった。(without 私の)
Since the sentence calls out 私のパソコン , that makes me think it’s the speaker talking (scolding) someone else.
I suppose it’s also possible to imagine a scenario where 私のパソコン goes with “I should have…”, where the speaker brought 20 other computers but forgot to his/her own computer. But that seems a less likely scenario.
my two cents. 
Hi @Marcus.W , you are right. This particular grammar point will be getting removed from N3 as soon as we add in the new writeups within the next couple of days.
Sounds good. Will the N3 point then also disappear from the review queue?
And perfect timing with the new N3 content as I’m just starting to look at the first N3 grammar points.
That is correct, the point would disappear from the review queue. Definitely good timing on N3!
Very good, thanks.
Very late but I would like to know this as well, it’s really bothering me LOL 
Like @EbonyMidget mentioned it’s ないで (JLPT N4) | Bunpro. What’s missing from that article is that ないで can also have an “instead of” meaning.
From A Handbook of Japanese Grammar:
V-ないで (instead of)
V-ないで is used to make a contrastive statement about two things. Means “do such-and-such instead of doing something else,” […].
So:
Oh okay, I see (idk how I missed that reply sry!). That explains a lot… I feel like that is a pretty important thing to include in the Grammar Point no? But thank you very much for the quick reply!