Upgrading TLS on server without reinstalling OS

I’m in a rather sticky situation.
Currently my server supports TLS 1.2 but not TLS 1.3 (security protocols).

It has the following installed:

Linux version 2.6.32-431.29.2.el6.x86_64 #1 SMP
OpenSSL 1.0.1e-fips
Apache/2.4.37

It also has a lot of valuable content with a special setup that I don’t want people to mess around with.

I read online that if I upgrade OpenSSL to version 1.2? and apache to 2.4.38? then I can get TLS 1.3.

So I tried a similar setup on my local machine then I tried updating OpenSSL from source and it claims I need new GLIBC libraries which makes me think that I need to replace the entire operating system for OpenSSL.

Is there a way I can upgrade OpenSSL without reinstalling the OS? or is there any other way I can enable TLS 1.3 with apache without reinstalling the OS?