If you're going to send the board to a fab, they have a set of design rules you need to follow like 10/10, meaning 10 mils min trace width, 10 mils clearance minimum. Generally it's ok to route between the pads if you can follow the clearance rule for your trace size. It's also perfectly fine to run a trace under a component, unless there's a specific reason not to, like noise coupling of some sort. For DIY PCBs I guess it depends on your skill, it's fine to do if you can make a pcb with finer traces but most people use wider ones for that. Another point to maybe consider is whether you'll be soldering around that point. Think about when you assemble the board, will it make soldering more difficult etc.