I recommend that you see your primary care doctor
about this issue.
It is normal to have some soreness and bruising at the site of an injection. In some cases, if a good sized bruised develops, this soreness could last a bit longer than just a few days. However, there are also some rare potential complications of an injection that your primary care doctor will be able to rule out for you.
First, sometimes, infection can occur in the skin around an injection site, with the needle hole serving as a site of entry for bacteria into the body. Signs of an infection, other than pain, would include warmth or redness in the area around the injection site.
Also, occasionally a large bruise
may form due to bursting of blood vessels from the injection. Usually this doesn't require any special treatment, but anti inflammatory or pain medications may be needed, and your doctor can help with this.
Finally, rarely, an injection may cause injury
to a nerve running down the arm, typically causes a pins and needles sensation.
Please do see your primary care doctor.