There are two major sources of stress for every senior: one of course being your thesis, and the other, the pressure of needing to secure a job for after graduation. My advice for dealing with your thesis is that its never too early to start writing. Start with small things that you can do early in the year like drafting the background and methods, rather than putting it off until the spring when you have most of your data. I would also get stressed when I felt behind on my thesis, and would avoid my adviser out of embarrassment of not being far enough along; don't do that. Keep talking to them because they really do just want to help you write a good thesis.
As for the pressures of having post graduation plans, I want to emphasize that you should not feel like you are failing no matter how late it in the year you secure something for post graduation. In the fall you will experience the annual whirlwind of seniors vying for consulting jobs, and in the spring there will be another large wave of fellow seniors getting jobs. Don't let any of this make you feel behind for not having plans yet; there are a lot of other seniors in your position as well, it's just that they don't go around sharing this information. Just relax, stay positive, and keep trying, and it will all work out.
Most importantly, try to not let either of these stop you from enjoying your final year at Princeton. Make sure to take breaks from the pressure and just enjoy being a senior. You earned it!