This happened to me earlier this year.
I aggravated it doing ab-wheel rollouts for the first time in a while. I was quite sore from them. A week later I felt a “pop” in the same spot - lower left ab - during the last rep of my last set of strict pressing. It hurt any time I sat up, but I did manage to squat 455 on it with no issue. I worked around it for a week or so before getting it checked out.
An ultrasound revealed it to be a “sports hernia” which isn’t like other hernias where something is poking through your abdominal wall. What happened was my lower left abdominal was partially detached from the pubic bone.
I just took it easy for a few weeks until the pain subsided, then I went right back to squatting, benching, deadlifting and yes, strict pressing. But I did not cease lifting while it was healing. I just didn’t do anything that hurt it.
I would recommend getting it checked out.