It depends. With ibuprofen in particular, the anti-inflammatory properties are beneficial. Initially inflammation is important for healing an injury, but too much inflammation is detrimental. Based on that I prefer to take ibuprofen if the inflammation persists, but not immediately after getting the injury.
Pain killers can also indirectly contribute to healing. If the pain prevents you from getting adequate rest, your body can't repair itself as effectively, so if taking a pain killer helps you sleep better that could actually help you recover from the injury faster.
For your specific situation, I wouldn't expect any painkiller to be particularly beneficial. If you feel pain only in certain positions rather than constant soreness that doesn't suggest inflammation, and if you can rest without feeling pain you wouldn't get any benefit from painkillers.
I would suggest finding a massage therapist who specialises in trigger points/myofascial release. It's something you could do yourself, but given the short time frame you describe a skilled practitioner is more likely to get you the results you need by the time you need it.
If that isn't an option, I would look into buying a foam roller. Lie on it with your back, find a point that hurts and steadily roll back and forth on it for no longer than a minute. You shouldn't necessarily be looking for where you feel the pain when you bend over, but for where you feel the pain from your bodyweight on the roller. Do it on both sides, and focus on your whole back. Do this several times per day. If it's not a serious injury it should get a lot better. You could even take the foam roller to the tennis tournament and do it between matches. Any time you treat muscle issues yourself they have a tendency to keep coming back for quite some time, but the temporary relief is often enough to let you do whichever activity it is you needed to do.
