I think it would be preferable to put aside whether house prices will rise or fall - it is less of a primary consideration when you and your child need somewhere to live, rather than an buying for an investment property.
Consider your overall financial strategy and future goals, and the stability and security of your own situation:
Do you have some emergency savings and a substantial deposit? Do you have debts? Are you in reliable employment and can you maintain a steady stream of income? Do you have the means to maintain a property?
These are things I would think about before worrying about fluctuating house prices and interest rates. They are somewhat of an unknown. What you can deduce is your own housing needs, affordability, your financial footing and future plans to build your wealth. Base your decisions on these.
A long term outlook will provide a much better decision - do you want to own? Do you understand the pros and cons of owning/renting? Are you wanting to stabilise your location and living situation as a single parent, reluctant to move again if renting is less than predictable - or do you want flexibility to change your mind?
In a few years time the worry of house prices/ interest rates will have settled down - in the meantime there could arise a situation of very little housing stock to choose from if sellers wait out the instability, or then again house prices may start to rise and make buying more difficult. Financial constraints on lending might tighten making mortgages more difficult to access. All of these things have happened in the past.
Take a longer term view of your assets, and your financial and housing needs and goals, and base your decisions on these.