You can definitely hurt a gigantic monster from the inside; It's actually the only way to get out of Tarrasque once you've swallowed it. So, if you apply the same rules (your character is blinded, reticent, has complete cover and suffers Acid damage each turn), it should be possible to adapt it to other monsters.
However, the fact that your character has complete coverage can cause problems, depending on how you want to use magic. Protection against attacks is also protection from help.
For more swallowing rules, I've actually come up with a D & D Basic guide that contains some useful rules that you can use. Big frogs and big toads are smaller than Gargantuan, but have rules for swallows. The Tarrasque is larger than Gargantuan, but has similar rules for Swallow. It is therefore logical that a gigantic creature has similar rules in this direction.