I’m looking for a science fiction short story. My memory is a little hazy but I believe the story was about a prehistoric young man who was traveling to return to his tribe and had to deal with giant bugs and the like. May have included giant mushrooms etc. I think I read it in the 80s or 90s.
You may be thinking of "The Mad Planet", a novella by Murray Leinster, first published in Argosy, June 12, 1920 (available at the Internet Archive); reprinted in Amazing Stories, November 1926 (also available at the Internet Archive) and Fantastic Novels Magazine, November 1948 (also available at the Internet Archive) and many other places. In the 80s or 90s you might have read it in Isaac Asimov's Magical Worlds of Fantasy 5: Giants. The full text of is available at Project Gutenberg.
The setting is not prehistoric but thousands of years in the future. Otherwise it matches your description, with giant bugs and giant mushrooms.
Here are your giant mushrooms:
He was treading cautiously over a brownish carpet of fungus growth, creeping
furtively toward the stream which he knew by the generic title of "water." It was the only water he knew. Towering far above his head, three man-heights high, great toadstools hid the grayish sky from his sight. Clinging to the foot-thick stalks of the toadstools were still other fungi, parasites upon the growth that had once been parasites themselves.
And overgrown insects:
The tiniest butterflies of former days had increased their span until their gaily colored wings should be described in terms of feet, while the larger emperor moths extended their purple sails to a breadth of yards upon yards. Burl himself would have been dwarfed beneath the overshadowing fabric of their wings. [. . . .] Not all the insect world was so helpless or so unthreatening. Burl knew of wasps almost the length of his own body who possessed stings that were instantly fatal. To every species of wasp, however, some other insect is predestined prey, and the furtive members of Burl's tribe feared them but little, as they sought only the prey to which their instinct led them.
From the acknowledgments page of the collection Planets of Adventure:
The Forgotten Planet was Leinster's rewrite and novelization of three novellas published previously: "The Mad Planet" (Argosy, June 1920), "The Red Dust" (Argosy, April 1921), and "Nightmare Planet" (Science Fiction Plus, June 1953). In the original first two stories, the adventure was set on a far future Earth. The rewritten novel version was first published by Gnome Press in 1954.
I wonder if this might be "The Forgotten Planet" by Murray Leinster? It was first published as a series of novellas starting in 1920, and first put into novel form in 1954. I found it in the collection "Planets of Adventure" (the link includes several sample chapters).
The story does include young man from a primitive sort of scavenger lifestyle, dealing with a number of nightmarishly large insects, from giant moths to dragonflies to spiders, and also enormous fungi (with equally enormous harmful potential, from poisonous spores and the like). He travels away and returns to the tribe, and sort of single-handedly moves them from scavengers to hunter-gatherers, and takes them to new living grounds.
This story is not, actually, set in prehistoric times but seems much like it narratively, the actual situation being a terraforming attempt gone astray, on another planet, but since the tribe didn't know that in-universe, well.