Should I go to an urgent care center?

Two days ago, I was attempting to do my nails and accidentally cut some skin next to my nail. I put Neosporin on it and let it be. Now, my finger is warm and I feel a slight throbbing pain every now and then. Some pus came out yesterday. It's most likely infected, but do you think it will go away on its own? I really don't want to go to the nearby urgent care because they have been treating covid patients there. I'm scared to leave my home let alone an urgent care center!! Do you think it is worth it to get antibiotics of keep doing otc?

Thanks for the help ladies! Will be making an online appointment tonight so I can video chat with my doctor.