The short answer
Yes. Randomly remembering an embarrassing thing you did — sometimes from decades ago — is one of the most consistently documented forms of everyday memory, not a rare quirk specific to overly self-conscious people. Studies that track memory as it happens in daily life, rather than asking people to recall it afterward, find these unbidden memories showing up regularly across ordinary days.
The research
Involuntary autobiographical memories are consistently found to be episodic and highly specific — tied to one concrete moment or scene — more so than memories people deliberately try to recall, which helps explain why a randomly-surfacing embarrassing memory feels so vivid and detailed.
— Berntsen, D. & Hall, N. M., Memory & Cognition, 2004
Why it feels less normal than it is
Part of why it feels abnormal is that you only ever witness your own involuntary memories — you have no visibility into how often it happens to anyone else, since nobody narrates their internal cringe attacks out loud. Research specifically comparing involuntary and deliberate memory retrieval has found the involuntary kind is at least as frequent, and in some studies more frequent, than memories people intentionally try to recall — directly contradicting the older assumption that unbidden memories are rare exceptions.
The specific, vivid quality is also normal
One striking, well-replicated finding is that involuntary memories tend to be unusually specific and episodic — a single moment, a single scene — rather than vague or generalized, more so than memories people deliberately search for. That's part of why a randomly-remembered embarrassing moment can feel so oddly cinematic and detailed compared to memories you actually try to recall on purpose.
When it's worth paying more attention
The frequency itself isn't a red flag. What's worth noticing is whether the memories are becoming more frequent over time, more distressing, or start interfering with concentration or sleep on most days — that pattern is different from an occasional, passing cringe, and is more useful information to bring to a professional than the mere fact that the memories happen at all.