Is my finger broken/ is it worth it to see a doctor?

I smashed my middle finger at the gym today with a kettlebell. It was numb for a few hours. now it hurts a fair bit (kinda throbs along with my heart beat) and the tip has turned blue. It's pretty tender if I bump anything with my finger. I still have good range of motion in my hands, can make a fist and spread my fingers apart. Here's a photo, https://i.imgur.com/mTW8O1K.jpeg

Should I see a doctor or can I just ice it and hope for the best? I live in America and have no money or insurance

Age - 26

Sex - Male

Height - 6'

Weight - 155

Race - not relevant

Duration of complaint - Today

Location - WA USA

Any existing relevant medical issues - none

Current medications - none