The money you receive as part of an insurance claim or agreement is generally not taxable. The IRS only applies income taxes, which is money or payment received that results in you having more wealth than before. Generally speaking, any settlement or judgment amount you receive as compensation for lost income is subject to income tax. The reasoning is that your original income would have been taxable if you hadn't suffered the loss of income, so any compensation intended to replace that same loss of income should also be taxable.
In most cases, payments received for medical expenses are completely tax-free. This makes perfect sense because it is not about money received by the plaintiff. Instead, medical providers who provide treatment are paid directly. All injury claims settlements include reimbursement for medical expenses.
Strictly speaking, this money is not taxable. Compensation for medical expenses only becomes taxable if you used those expenses for a tax deduction on your prior-year tax returns.