Added Outlet to a GFI Receptacle covered circuit
The fridge/freezer are a red herring.  Cable length is a red herring.  These are not the problem. 

Here, simple logic applies.  It worked before; you changed it; and now it doesn't work.  I'm sorry, that's inescapable, and it tells us where to look. 

Noting your credential, it may be a bit afield of mains wiring in buildings. Mains wiring is weird, that's the only way I can really describe it to an electrical professional.  Different things are done for their own set of reasons.  If you deep-dive into the gory details of the reasons, you eventually find they are well-founded - but until you do, they seem arbitrary and stupid, and it is tempting to ignore them and do what seems right. 

In your case, first, go after the forehead-slappers.  Look in both your new box and the box you tapped from (which I assume is not the GFCI) -- and look for anything out of order, but even more, focus on that floppy-doppy bare ground wire touching any of the screws. If you're using backstabs, stop using backstabs, but make sure you haven't left any bare wire sticking out for a ground wire to snag and touch.  Contact between neutral and ground is super-bad.  Normally it's a "silent but deadly, but in the case of GFCI, it will result in instant trip.

One common tactic is, after attaching all the wires to screws, run all the other screws down and wrap tape around the receptacle so it covers all the screws.  



Now if you did tap the GFCI device, you are using the LOAD terminals but not correctly.  You must use them for both hot and neutral.  Using LOAD hot and LINE neutral or vice versa is a guaranteed trip.  The nut of what's going on with GFCIs isn't that hard to understand: 



Disregard the dashed lines, those are for extra phases on GFCIs equipped for extra phases.  Do note the fact that the GFCI device completely ignores ground.  

A GFCI+receptacle combo device is extra hard to understand because it's doing 2 totally unrelated things at once, like a destroyer that's a fleet oiler, or an E-2 that also does Prowler-style SEAD.  What's actually happening is that it's exactly the black box with supply/LINE and protected-zone/LOAD -- except it also has 2 sockets hardwired to the LOAD terminals.  (it still doesn't use ground, but the sockets use ground.) 

On the right side, both hot and neutral are in the "protected zone". Most of my work is in conduit, and I intentionally use a different color - brown and gray - for protected-zone hot and neutral. Every load must tap protected-zone hot and neutral together.



Now: you may have a wrong read on the issue with GFCIs and refrigerators and freezers.  It's not that they're "touchy" (by which I read: more likely to trip GFCIs all on their own).  It's that there's a very severe risk of a nuisance GFCI trip for any reason destroying valuable food.   A fridge is no more or less likely to trip a GFCI than any other motorized device. 

However, Fridges/Freezers on a well-grounded circuit are not the use-case for GFCI, they are the exact opposite of the use-case. 


GFCIs are there to protect humans from accidental shock. The grounded steel chassis of the fridge/freezer already does that. 
GFCIs protect where humans are likely to come in contact with AC-energized parts.  All that stuff in a fridge is at the bottom rear, where you can't get within 6' of it if it's installed in kitchen counters
GFCIs protect humans from 2-prong ungrounded equipment. Fridges are well-grounded. 


Simply put, Code does not call for protecting fridges with GFCI.  This discussion (uselessness of GFCI and cost of lost food) has been had within NFPA, and they chose to exclude fridges from GFCI requirements. The only way fridges get haled into GFCI is when they are placed in rooms where all receptacles have to be GFCI, and even then, only because you are choosing a cord-and-plug connection for your appliance.  

Hardwire it, poof, GFCI requirement goes away. 



So, because of the risk of food loss, having a fridge/freezer on GFCI is a bad idea. What's an even worse idea is having the fridge/freezer on a shared circuit with general receptacles.  So yes.  You should definitely run a separate dedicated circuit to power the fridge/freezer.  

And since that might require pulling a permit, you should go have a talk with your AHJ (the guy who issues the permits) and ask him if GFCIs are really necessary on receptacles that serve only fridge/freezer.  He may say "That's fine, 1 circuit, 1 socket" -- Because usually these conversations assume ONE refrigerator OR freezer and so require a 1-socket receptacle so you can't plug anything else into that circuit.  So you'd have to have the "I have both" discussion and see whether he'll allow a duplex receptacle or want 2 dedicated circuits with 1-socket receptacles.  If you've got the panel space, Romex is cheap, so why not. 

Plan Charlie, is hardwire the fridge-freezer, by having their cords enter a junction box with a quality strain relief, then splicing in the junction box. This means lopping off their sockets, or my preference, go to the electrical supply and get wet-rated cordage of appropriate rating and replace the whole cord, saving the old cord for when you sell it.