You probably could get sub 15 without full PLL or OLL with years of practise, but you could aswell be sub 10 with learning them. I don't know what's your current average, but after 30-25 seconds full PLL is probably the easiest way to get faster.
It's not even hard to learn PLL, just learn one or two, then do normal solves for a day or so and use the PLL algs you've learned. Practise until the new algs are in your muscle memory, and only then you really know the alg.
That really helped me when I was learning PLLs, first I tried to learn too many at once and I was just confused. For me it took like a day of practising until the new algs were in my muscle memory and then it was easy to learn another alg.
Full OLL isn't as important, but after PLL you should start learning the easier OLLs first. The easiest ones are really easy, and after a while learning new algs becomes much easier.