Here are some photos. I planted some seeds and this is what they've become. Any tips? Is it possible to get watermelon at this time of the year or?

What are they in?
An inch or two of potting soil?

I grow watermelons fine... But I'm in the sand.

If you are in the heavy clay, I'd dig down into the clay at least shovel deep, and work in lots of compost / manure, and try some new seed. Should be plenty of time to get some watermelon, before frost.

Incidentally, watermelons require all day direct sun... If those are in the shade, that could be part of the problem.

Do you think there is any possibility of getting any fruit from the current plant? honestly I am not sure how deep thi soil goes down. that said I do believe I have more of a clay soil. And they are not in shade. they get direct sun. I feel like part of the problem is either that I am watering too much or I am watering too little LOL I can't figure out which one it is

Most likely not. Last year I had much healthier plants than yours and I got tiny fruit, uneven, so I threw them away, no bigger than a tennis ball.
Have you thought about giving your plant a bit of fertilizer?

I've always found that watermelons grew better for me in the drought.
when they got too much rain, the fruit split open.

really feel like the problem is shallow soil.

whether you attempted to fix the current bed or just dug some new soil is up to you.

but... I'd strongly encourage digging beds at least shovel deep.

Concur; Watermelons originated in the desert. Their major requirement is space to roam and deep loose soil for their root system. They love sand, hate clay. I expect this vine is too severely stunted to do much at this point. Like Stone I am in the sandhills, But I still double dig my watermelon hills.