HELP! I got bit by a dog, now what?

Distant neighbor’s dog bit me. EMS said maybe get a tetanus shot since I hadn’t had one in over 6 years, I for sure had one in 2003. I read online that the vaccine stays effective for a looooong time. Just topical treatment or go get vacc’d? Or??

Also, I took a dive yesterday and got some lacerations to my underside of my hand attempting skateboarding for the first time. If that plays any role in deciding whether tetanus is worth the precaution.