Namecheap's BasicDNS defaults new records to an 'Automatic' TTL, which behaves like roughly a 30-minute cache. That is why editing an A record or adding a TXT verification string on Namecheap usually takes effect faster than the blanket '24–48 hours' figure their help articles quote as a worst case. You can override the TTL per record if you want tighter control, dropping it to a few minutes before a planned migration.
Switching your domain from Namecheap's default nameservers to a third-party DNS host — or enabling Namecheap's PremiumDNS — is the change that can take the full day or two, because the nameserver delegation is cached at the registry level rather than by ordinary resolvers. If you just moved nameservers and things look inconsistent, that is expected: keep the old and new zones serving matching records until every location agrees.
It is also worth checking whether you are editing the zone that is actually authoritative. If your domain still points at Namecheap's nameservers but you configured records at another provider (or vice versa), nothing will appear to propagate no matter how long you wait. Verifying the live NS records first, then the individual record, tells you whether you are looking at a propagation delay or a misconfiguration.