So whenever I do standing military press with any weight, it seems to kind of tear at my back. Not my lower back, but maybe my upper or middle. Anyone with similar experiences?How do I avoid this? Am I using proper form?
It may sound unnatural, but squeeze your glutes (butt cheeks) as hard as you can during the lift. It will prevent your back from bending. Stronglifts explains it very well. The section "Common Pains" explains how to avoid injury.
Hard to say anything definite without seeing a video or pictures but I'm thinking it could be a combination of a weak core and faulty technique.
Try doing the plank and back raises, without and with added weight, and see how it feels. Does it hurt similarly?
As for diagnosing your form: look in a mirror to see the curvature of your back, as you're pressing. It should be pretty straight – otherwise you risk overextending and hurting your back.
You can also try laying down on your back and having someone put their hand under the small of your back. Tighten your core and press down against the hand – that's the form you want to press from.
If the pain is located very high up, you could experiment with your grip width. Does wider feel better than smaller?
Also try to push your elbows out, so you're not pressing in front of yourself as much as straight from the sides.
Hope that helps! Else please upload a video so we can check your form. Of course, if it keeps hurting I would strongly recommend also seeing a proper physio in person.
Your primary concern here is obviously to identify the cause of your pain. To investigate this, you will need to use exercises which are broadly similar to the military press, compare which of them cause pain, and use these as a basis from which to locate the issue.
For instance, in this video by Jeff Cavaliere, he uses barbells, dumbbells, and cables to demonstrate the differences to the body by the different approaches to overhead press exercises. As he observes the cable press at the end provides a massive additional effort to the core, so if your core is the problem, you are likely to notice a difference. Alternatives to these approaches are using bodyweight exercises such as the upside down press against a wall, or the pike press.
If it is a core or back problem, it is highly likely that you will feel a problem during core or back work as well. The question then is whether or not you have a balanced plan which works out your whole body, from which you could make a judgement. Other indications could be from for example barbell squats. If you can do barbell squats without a problem, then your posterior chain can be ruled out as having the issue.
If you need to find this problem by yourself without professional help, eliminating the possible culprits will probably be the best way of finding what the problem could be.