No, Kiruko is not pregnant, Ishiguro literally confirmed on his Twitter that Kiruko had their period when they left the Ministry of Reconstruction in Nara with his own in-universe calendar.
https://x.com/masakazuishi/status/1713242006355665083
I don't think being Japanese has anything to do with a senior citizen (who already acted like a
chūnibyō) who's brain got transplanted to a younger body that's now going through puberty, being shocked/embarrassed when she assumes one of the youths (who is old enough to be her grandchild) is coming on to her.