Hello and welcome to Healthcare Magic. Thanks for your query.
You seem to be having a 'paronychia' (nail bed infection) with an underlying abscess
formation (i.e. an infection with localized collection of pus). You will need a small surgical procedure to drain the abscess and if the nail is also infected, to remove the nail also. Further antibiotics or other ant-inflammatory medication are unlikely to help, and the infection will subside only if the pus is drained out. So, please consult a doctor, preferably a surgeon, for further treatment.
Wish you all the best.