The maximum limit of the pouch and storage capacity can be increased via upgrades throughout the game.
Remember to actually USE the things you're gathering, to make improved weapons, armour, and cook healing items to help with combat. And know that the best defence is outright avoidance!
Also note that green and blue tonics can be useful to improve movement / dash speed, or increase your capacity for carrying resources.
There's ways and means to make things easier for yourself, so do give them a try!