I had a wooden splinter on my left ankle doctor said no tetanus, need second doctor opinion

I had a wooden splinter on my left ankle, I was sitting at a wooden deck next to a ferry stop place, then when I want to get up my left ankle scraped on the wooden deck and a wood splinter got in my ankle. It didn’t went in vertically but went in horizontally across the skin. Here’s a pic of the wound after I manage to take the bigger piece out
It only bleed a little after I took the big piece out, and as you can see there’s still smaller pieces left in there so I went to a doctor, the doctor manage to take all the pieces out with local anesthetic. The doctor open up the wound and there was some bleeding happening, the wound it’s now covered with a gauze. I asked the doctor whether there is any risk of tetanus, as I haven’t had a tetanus shot in more than 10 years (in fact I don’t think I’ve ever had one?), as I don’t like the idea of having vaccination and their possible side effects. The doctor said it should be fine without one as it’s not a deep puncture and the wooden deck doesn’t have any rust etc. but I would like to ask for a second opinion as I’m quite worried about tetanus.I’m 26 year old female, no known medical conditions.