Hello and thank you for asking your question on just answer. My name isXXXXX will try to help.
If you removed the engorged sack, what are you seeing now?
The sack should have been attached to a black/brown mouth part.
It sounds like a horror movie. : ) It will be fine.
Ok, get a small cup of isopropyl alcohol. The kind you buy at the drug store. Put the pods in there because it will kill them. Leave them in there overnight.
Then you will need to get the tick's mouth parts out of Buddy's skin. Get a tweezers and grasp the tick's mouth parts as close to the skin as you can. Pull out at approximately a 45 degree angle. It will feel like it is stuck but keep on pulling and then the mouth part will come out.
If you can not get all the mouth parts out it is not the end of the world. Buddy's body will form a little fluid pocket around it similar to when you get a splinter. Then the fluid pocket will break open releasing the foreing material. Now if there is a large amount of fluid, redness, and heat then he should be seen by a vet.
Clean the area with antibacterial soap.
Then apply an antibacterial ointment, such as neosporin, three times a day.
Since the tick was in there long enough to become engorged, there is a possibility that the bite will become infected. If it does, it will become red, hot, and swollen. It will need to be treated with oral antibiotics.
There is also a chance that he will get Lyme's disease or another tick borne disease. Signs of this are lameness, fever, lethargy, and not eating. This can be treated with antibiotics as well.
Make sure you wash your hands thoroughly with soap and water.
I think you are right.
The vet sounds like the best idea.
I will forward this to customer service so they can refund your deposit.