I know you're looking for help online but I think it's time for you to go see your family physician w/the above complaints. Back pain w/vomiting blood, headaches & weakness is not something to treat w/stuff in the medicine cabinet. You didn't mention your age, pregnancy status (yes/no), how long this has been going on, what other medical/surgical issues you have, and what medications you're taking (or are allergic to). These are all things that physicians need to ask & know about you in order to really be able to help you.
Pneumonia can cause back pain. Plus anyone who coughs hard enough can throw up and break a blood vessel in the throat/breathing tube and see blood in her phlegm & vomitus. If there's enough bleeding, you can feel weak from anemia, especially if this coincides w/your menses.
If you've been traveling in a car/bus/airplane for a long period of time or just recovered from an operation, you might have a clot in your leg (DVT) that breaks lose and travels to your lungs (back pain) and causes vomiting blood (from coughing - see above) but this is typically associated w/chest pain & shortness of breath (think Serena Williams).
Stress can cause muscle tension leading to back pain & headaches. But this usually shouldn't cause vomiting w/blood (unless you're really stressed?), unless you broke a blood vessel as mentioned above.
Of course, if think of John Ritter, and depending upon your age, an aortic aneurysm could erode and cause back pain & vomiting blood w/weakness from loss of blood. But in that case, it's doubtful you'd be typing your question and waiting for an answer. I'm not sure how a headache would fit into this scenario anyway.
As physicians, we are trained to look for a single answer that explains everything, rather than searching for several different solutions, one to account for each symptom/complaint.
I mentioned in a recent post that vomting blood could stomach & esophageal (swallowing tube) ulcers can cause blood in vomit. But so can bloody noses, too!
Weakness could be from loss of blood, which is never a good thing. So could the headache. For those who like to think worst case scenarios, some cancers can spread to the bones & brain, leading to back pain & headaches along w/weakness.
Having thought about all this, my conclusion remains the same. It's time to go see your family physician. Don't wait! Good luck!