Fear of needles (or trypanophobia) is quite common. For most people, this is rather mild. You might feel some anxiety as the syringe penetrates your skin, but this quickly subsides as you realize that the worst is over. For other people, it's far more severe, triggering a sense of dread and panic. A fear of needles can be particularly problematic when it comes to pain relief for dental procedures.
An injection of novocaine is common practice prior to certain forms of dental work. It's quick and effective, but this is of little comfort when you're affected by trypanophobia. However, it's not as though your dentist will forego pain relief when it's undeniably needed. Fortunately, there are other options that don't require a syringe.
Pain relief can be administered orally, but the timing can be problematic. An injection is delivered directly into your bloodstream, whereas anything taken orally must be absorbed via your stomach, which can take a bit longer. When trypanophobia is an issue, you might be able to receive pain medication prior to your appointment. You would then dose yourself as per your dentist's instructions, and this can happen at home before you leave for the dental office. Although it avoids a syringe, you might have to make multiple trips to the dentist (picking up the medication and then returning for your actual appointment).
Sedation dentistry is also an option. Some forms of sedation dentistry still require an injection but not all. Depending on the nature of the required procedure, nitrous oxide can be sufficient. This is a gas, and all you need to do is inhale. While this is a type of sedation dentistry, you will not be fully sedated, as the gas offers what is known as conscious sedation. This means that you remain awake, although the gas calms you and disrupts your pain receptors.
Some dentists offer electronic pain management. This involves electrodes being affixed to your gums, which then strategically release electric impulses to block pain signals. There are different machines, offering different levels of electronic anesthesia, and this might not be suitable for a particularly invasive procedure. However, for many forms of dentistry, electronic pain management can be highly effective.
In short, remember that a syringe isn't the only form of pain relief available for dentistry, and so you shouldn't let trypanophobia prevent you from visiting the dentist. Speak with a local dentist about what options are available to you.