Yes. A big possibility.
Yes. Depends on what medical conditions you have. You might be prone to develop clots, have other risk factors- some are congenital. Obesity, on birth control pills, inactivity, are some common risk factors.
No. Aspirin is a blood thinner and would not cause a blood clot. Motrin should not cause a blood clot either.
Blood clot. No, this is not the first thing you think of concerning the cause. Please submit a lot more information about you and the back pain in order to give more help.
No. Whatever it is you need to take it seriously. Get your doctor make that determination.