If it's been three months since you think you have been exposed, symptoms would have appeared by now. Most cases show symptoms after one month. Generally the vaccine is given within four days of exposure. If you do get the vaccine, you will probably start to get scared that you did not get the vaccine soon enough. You could also get scared that the vaccine actually gave you rabies or did not work.
I'm just posting from my own experience, because about 2 months ago I had a fear that I was exposed to rabies, and the day after I thought I was exposed, I convinced my mom to let me go get the vaccine. I later got the additional doses on the 3rd, 7th, and 14th days (you need to get 4 of them). About a month after I started to get one of the symptoms of rabies (difficulty swallowing, sore throat, and a feeling of your throat closing up) and I was terrified for about a week that the vaccine gave me rabies or did not work. The fear was just as bad as the day between I was exposed and I got the vaccine. It eventually cleared up and I haven't been scared of rabies since.
Those are two things you need to consider before you get the vaccine.
Also, the vaccine is very expensive. I later found out that the shots would have costed about $1,000 each for a total of $4,000 if my insurance had not covered it. If you have good insurance it's nothing to worry about though. And my mom said that even if we had to pay for them I still would have gotten it because I would die if I was exposed and did not get them.
I read your story, about the raccoon, if you were not bitten, you do not have to worry. The only way you can get infected is if the animal's infected saliva gets into your blood stream.