A social construct is something that is produced artificially through social interaction to try to establish some rules to social interaction. For example, gender is considered a social construct (as opposed to sex, which is biological) because of the fact that it serves a social role within interactions.
Morality by default is absolutely a social construct by conclusion.
The problem with morality is that personal morality and social morality often conflict in fringe issues. For example, a major issue that the transgender community faces is affordable access to treatment options. To a transgender person's morality, they deserve affordable treatment options because they suffer due to not being able to access treatment. Social morality may disagree though, outweighing the benefits for a minority to help better support society in general. Depending on the social morality, the transgender person's wishes may be granted (some cities/states/ect. do have laws to make financially accessible treatment for transgender people a reality) or denied.
This ends up causing serious flaws. The most noteworthy example I've noticed is probably regarding those who are born blind. Blindness by default is regarded as negative in society, and in general, most people try to "cure" or "fix" blindness, instead of assisting people with blindness. This ends up being a very serious problem because not only is a cure for all forms of blindness simply not possible right now with current technology, and not only is it neglecting problems that, if fixed, could help all blind people live independently, but also that some blind people don't really want to be sighted.
Many people born blind are curious about gaining sight but are afraid of having it for the long term, because it's such a foreign sense to them – to them, blindness is completely natural, and sight is a very unusual and exotic experience. This is difficult for most sighted people to empathize with unless they sit down and try to personally understand why they feel that way. It may seem more morally incorrect to allow those born blind to continue being blind and instead help improve blind accessibility, but this is based on a social standard that "blindness is bad", without really consulting how an actually blind person feels.
All in all, morality doesn't work ultimately with every situation but it's a decent general gauge. Just don't rely on it completely since it can fail in extreme cases as pointed out.