Hi Karl, welcome to OrchidTalk! Your phal is growing a baby plant ( keiki ). Usually it is a good idea to cut off the spikes after your phal has bloomed. I recommend cutting them off at about one inch above the plant. Some people leave them on and perhaps cut them above the third node in hopes of getting another set of blooms. This sometimes works but the blooms are reduced in size (usually) and your plant uses lots of energy it could use for growing stronger roots or replacing an older bottom leaf.
It is time to repot and from the color of your orchid's leaves, it could use a bit more light. Phals like lower light levels, but a bit more light would perk up the color to a lighter green. Also, from the leaves that appear to droopy on the right side of the photo, you may have some root issues to clean up a bit.
Here is an article to help with your Phalaenopsis : Growing the Phalaenopsis Orchid (Moth Orchid)
Best of luck to you and again - Welcome to our Community!