Even if the window is south facing? (I was mistaken when I put west.)

Most culinary herbs require "full sun." Full sun never equals a sunny window. The plants will not be as robust and healthy as outdoor grown plants.

Your basil will get tall and skinny and fall over.

IN Phoenix - same zone as yours, I grew it in full sun and it thrived. It did OK with afternoon sun, but outside where the light is much brighter.

Are you in an apartment? It grows well in big pots outside unless you get a bad freeze. I had it overwinter a few times.

I am not in an apartment but I need to constantly see the plant to not forget about it and if I were to put it outside my dogs would pee on it, even on the porch.

If it were outside forgetting about it would be less of an issue. You would not need to fuss over it so much. Your herbs are never going to be truly happy in that position whatever you do to them. This applies to both your Cilantro and your Basil. And the former will almost certainly bolt very quickly if it is not thriving.

If it were outside my dogs would pee on it as I said in my previous comment.

Full sun conditions do not mean a shaded southern window sill. Full sun means that light can strike a plant from above, from the back and sides.

I'd suggest that you consider some pretty indoor foliage plants, most are able to thrive on a sunny windowsill.

If culinary herbs are still your heart's desire, consider THIS , or similar. It's equipped with a light that can be adjusted as your plants grow.

Outdoors in full sun would be best for your basil and cilantro.
There are ways to get the pots up where the dogs can't get to them. Shelves, even if it's just landscape beams or decking boards on concrete blocks will keep things above the dogs. Hanging planters are another possibility. Hang pots on "shepherd's hooks," or you can repurpose an old swing set frame as a frame to hang a bunch of hanging planters.

They are doing fine now. I just had the bad luck of planting them when there was nearly 3 straight weeks of pure clouds and rain and I forgot to fertilize them.

I grow all my herbs in pots outdoors that are raised up off the ground by either bigger pots or a wooden shelf. One of these days I'll hook up an irrigation system so they get watered regularly.