Foxtails( which are a grass seed) can dig in pretty fast and then they will keep traveling and can even make it to vital organs so it is best to get to a vet ASAP if you think your dog has a foxtail and if it is early enough they can probe around and get it or even sometimes flush it out if not it takes surgery to find it and remove it.
I have only had one dog get one and that was Jazz I had noticed she had been biting by her tail and being she did not have fleas, ticks or any skin issues I took a look and there was a small swollen bump with an obvious hole in the center so I thought Foxtail. I called the vet and they were booked for the day but being it sounded like a foxtail one of the vets said she would give up her lunch so told me to bring her right in. She ended up doing a minor surgery and found the foxtail so my guess had been right on.
This is why I am trying to encourage the owner to go to the vet as it would be cheaper to get it out now if it is a foxtail as I have never seen a bee sting look like this and he just keeps saying I think it is a bee sting maybe two of them
We will be at the dog park soon and see if he has done anything yet.