Am I technically allowed to look up cards during a Magic tournament match?
You can't lookup things on the Internet during a match per MTR 2.12:


  At Competitive and Professional Rules Enforcement Level during drafting, deck construction, and playing of matches, players may not use electronic devices capable of taking and storing notes, communicating with other people, or accessing the internet (with the exception of taking brief personal calls with the opponent’s permission).


As for the Torrential Gearhulk. I've asked a judge at a Standard PPTQ Tournament (Competetive REL) if it's enough to name a card by describing it as "Blue Gearhulk". His answer was that it's OK, because there is exactly one card that can be described as "Blue Gearhulk" in the sets permitted in the format we are playing. This is per MTR 3.6:


  A card is considered named in game when a player has provided a description (which may include the name or partial name) that could only apply to one card. Any player or judge realizing a description is still ambiguous must seek further clarification.


MTR 3.6 also clarifies that:


  Players have the right to request access to the official wording of a card the can describe. That request will be honored if logistically possible.


So yes, you can ask about the card.