Thank you for the additional information.
If he is holding the foot up only when going in the grass and is licking the paw then I would be concerned that either he received some type of bite or sting when in the grass or that there may be something such as a fox tail( type of grass seed) stuck in the foot. I too live on the gulf coast and we have seen a few dogs recently with fox tails in the feet and face. If that is the case you may not be able to see it. Sometimes they will work themselves out the top of the foot but in some cases we actually have to sedate the dog and make a tiny incision to find them.
I am concerned about the not eating as this is not normally a problem with a simple bug bite but some dogs will stop eating if they are in pain.The fact that the pain is getting worse is also concerning and as mentioned above I would be more suspicious of something stuck in the foot.
Aspirin can also cause them to loose their appetite and this is not something that is recommended for more then 2-3 days as it can cause stomach ulcers. The normal dosing for this is 5mgs per pound of body weight not to exceed 10mgs per pound. I am not sure how much your little one weighs so be sure you are not giving to much. It is also important that if he needs to go to the vet that you tell the vet that he has had aspirin as this prevents the vet from giving dog safe anti inflammatory medications for 7 days.Click here for information on the use of aspirin in dogs and possible side effects. LINK
What you may want to try is stopping the aspirin and try oral Benadryl at a dose of 1-2 mgs per pound of body weight every 8-12 hours. Soak the paw in epsom salt water for 5-10 minutes 2-3 times per day. For a small dog the easiest way to do this is just put a small amount of water in the sink and allow them to stand in it.
Offer a bland diet for the next few days of boiled chicken or hamburger and rice in small meals several times per day.
If switching to the Benadryl and soaking the foot does not show any improvement in the next 3 days or the appetite does not return once stopping the aspirin then I would suggest having him seen by the vet.
I hope this helps and he feels better soon. Please reply back if you have additional questions or concerns.