I just came across your problem a few minutes ago, and thought I would put in my 2 cents.
I have been a dental assistant for a while now, and I have seen your problem quite a few times. You said that you got your dentures a week ago? Did you get any teeth extracted to get these dentures? If so, it will take a while for your gums to get back into working order. If you didn't get any teeth pulled, and they are new dentures, your gums will still be tender and swollen, I.E. your dentures will not fit properly, and food gets caught under the denture.
I recommend trying fixadent to your dentures for a couple of days. If that doesn't help, you should go back to your dentist and have him/her do some adjusting/trimming to your denture. Also, ask for something called a soft reline. It is a soft coating that gets put into your denture that will help them naturally stick to the gum without using any adheasives.
Good Luck!! :0)