Don't go installing software from sources unless you really know what you are doing, and there is no other way. Not on an enterprise distribution for serious use. And much less critical stuff like OpenSSL.
Note that in Red Hat Enterprise Linux (and its derivatives, like CentOS, Scientific Linux and Oracle Linux) the software versions often look old. They are the versions Red Hat selected way back when they cut RHEL X.0, and they will only upgrade to newer versions during the decade or so RHEL X is supported if there is absolutely no other way to fix bugs. Red Hat people backport fixes and patch bugs in what they ship, the code internally probably looks much more like the latest version than the original one, but the all-important external interfaces are rigurously kept. Rest assured that even if your package version is the all time champion in CVEs, what you have installed is not vulnerable to those problems.
You need some apache functionality, have you checked it isn't available for your installation? Have you looked at EPEL? Maybe it is available in the next version (RHEL and CentOS have several currently supported versions simultaneously, check the latest)?