This was written by the founders of Carter Lewis and the Southerners, John Carter and Ken Lewis. I wrote about their excellent song Sweet and Tender Romance here. https://am-records.com/2020/08/28/carter-lewis-and-the-southerners-sweet-and-tender-romance/
Can’t You Hear My Heartbeat (note, no question mark, though it should have one) was recorded in 1965 by the US girl group Goldie and the Gingerbreads, produced by Alan Price, and it got to No 25 in Britain.
This is a mimed version with slightly inferior sound
and this is the record.
Herman’s Hermits also recorded it in 1965 (with Mickie Most as producer) and obliterated the Gingerbreads in the US, reaching No 2. This must be the worst ever attempt at miming, and the track is rubbish compared with the Gingerbreads.
Marianne Faithfull did quite a sweet version on her 1965 debut album Marianne Faithfull.