Potted moonflower and morning glory plant question

[Justusla]

I am fairly new to the world of gardening and acquired some morning glory and moonflower seeds which I planted in pots at the end of May. The seeds sprouted and the vines have taken off but I am concerned that I should transplant the plants to a bigger pot/container/outdoor garden. Can I leave them in the existing pots? There have been no signs of buds/ flowers and recently white spots have appeared on the leaves, should I be worried? I water them every other day and they are in a well lit sunroom (south facing room).