The UK had plenty of money, or at least sufficient to ensure that you and millions of others do not need to be poor.
what is wrong, and is likely to stay wrong, is the distribution of the UK's wealth.
This 1,000 times over.
The EU is essentially a trading bloc. It has limited powers mostly to do with food standards, environment, health and safety and some workers' rights. This is misunderstood by many people. The EU can't dictate to any country how it distributes wealth between citizens.
So, for example, whilst we were a member of the EU we could join in to say how Italy or Germany should safety check ingredients in food. However we could not join in to say how much child benefit in Germany should be.
In the areas where we did delegate powers the EU did do some good that would benefit a single parent. So for example when I was a single parent (20 years ago) I directly benefitted from the increases in maternity leave and pay. Other help came from minimum standards of holiday pay, unpaid parental leave, working time protection and Equal pay provisions.
I think these protections are valuable and people like Liam Fox have already said they'd like to deregulate workers' rights outside the EU as they are seen to impede commercial profit.
Turning to money although EU membership didn't control how the U.K. distributes its wealth - membership did give unrestricted access to one of the largest trading blocs in the world.
On any of the government scenarios studied in their impact assessments the U.K. as a whole will be financially worse off after Brexit. As TM said the people voted for pain.
However the main thing that will affect the OP is how the domestic government distributes the wealth left. My bet is that Brexit will be used as an excuse for more austerity for decades to come.