You can use this tool to check if your certificate is affected by any recent Let's Encrypt incidents. Enter your hostname, and this tool will connect to your website, check the currently served certificate, and inform you if it is affected and needs to be renewed.
Switching to the serial tab, you can enter your serial number to see if your certificate is on the list. Searching by serial will only inform you that the certificate is non-compliant, not whether that certificate is currently served by a web server.
The API gives examples of how to query the Let's Encrypt API for this same information using the ACME Renewal Information extension.
CERT=certpath.pem
ARI_ISSUER_SPKI=$()
ARI_ISSUER_DN=$(openssl x509 -noout -issuer -in ${CERT} | sed 's/issuer=//' | openssl sha1 -hex | sed 's/(stdin)= //')
ARI_SERIAL=$(openssl x509 -noout -serial -in ${CERT} | sed 's/serial=//')
curl https://acme-staging-v02.api.letsencrypt.org/get/draft-aaron-ari/renewalInfo/${ARI_ISSUER_SPKI}/${ARI_ISSUER_DN}/${ARI_SERIAL}