For your own safety you should only consider service by Apple or an Authorized service provider. They will use approved spare parts from official sources, and you will not get the risk of untrained and unapproved service using parts of doubtful origin. In the case of batteries this is particularly important, because counterfeit lithium batteries can become unstable and catch fire without warning.
However, your phone is showing 87% which is still above the 80% level where Apple considers it is beneficial to replace the battery. Unless your iPhone is still in warranty or AppleCare cover, the best advice would be to continue monitoring battery health and working charge life for a few weeks before you make any decisions.
If you still have warranty or AppleCare, or you decide to ignore my suggestion and change the battery now, Contact Support to arrange getting your iPhone examined for Apple’s official diagnosis and a quote to replace the battery. From memory the USA price is around $79, and rouhly equivalent in other currencies and regions.