See my answer on the infectious disease site.
Yes, make an appointment to see your doctor. The redness on the finger and the fact that some puss came out, indicates that there is an infection there. Infections can spread, so it is best to get it seen to.
Your doctor may prescribe an antibiotic cream to apply to your finger or antibiotics to take by mouth.
In the meantime keep the area clean and dry.
If it is that way tomorrow, then yes, see a doctor, in the meantime, put some Neosporin on it after washing it well, also, put a band aid on it to keep it from further infection.