Can I upgrade to any latest iPhone if I purchased my iPhone X on August?

If you paid full price for the phone, as opposed to any of the other programs, you can trade it in, or sell it yourself and use the proceeds to purchase your upgrade. Given the information you have provided, it is difficult to say. See this, Trade in with Apple GiveBack - Apple

Check your upgrade eligibility > iPhone Upgrade Program - Apple

PandasticPanda wrote:

I’ve purchased my iPhone X in early August and was wondering if I could receive an upgrade as of getting one of the new phones.

Upgrade through who your phone carrier or Apple? Did you sign up for Apple upgrade program, if so what does it say about upgrading? If through your phone carrier contact them.