The stick is just in the beginning of the game, as it's part of the quest you should have it. Look at your inventory just in case.
Anyway, if you want to survive you should switch to a falchion ASAP.
Hope this helps.
I am in swamps. I realized that it was difficult to keep a pet in grasslands because it got hurt quite often and moreover two antidotes had to be used instead of one. So, I choose a sand beetle as pet and allowed it to be killed. Now, I can go wherever I want to. I helped the most in forest. It saved me a lot of antidotes and I could sell the berries and fruits for a fortune.