It depends on the state and policy guidelines.
Typically, Uninsured Motorist Bodily Injury coverages would not cover your or the people in your vehicle if you were at fault in an accident.

Typically, Uninsured Motorist Bodily Injury (UM) covers you, the insured members of your household and your passengers for bodily/personal injuries, damages or death caused by another driver who was at-fault and uninsured or a hit-and-run driver. If you are involved in an accident where the other driver is at fault but has no insurance, this policy will cover your medical expenses, up to the limit on your policy.

So you cannot make a claim for yourself or your passengers under UM unless you were in an accident with at uninsured motorist who was at-fault for the damages to your vehicle and injuries to you and your passengers. If you were at fault then UM would not cover this situation.

Your own bodily injury liability coverage may cover injuries sustained by your passengers though. Who and what Bodily Injury Liability (BI) will cover can differ according to state laws insurance policy terms. Each auto insurance policy will define the scope of coverage for Bodily Injury Liability coverage.

If you have Personal Injury Protection (PIP) on your policy it may extend to your passengers. Medical Payments (MP) usually will also extend to your passengers in case you have this type of coverage.

If you were at fault in an accident where you and your passengers sustained injuries you should read through your car insurance policy and speak with your agent who knows the specifics of your policy to what coverages you and your passengers may be able to make claims though.

There may be some states where UM does extend to drivers and passengers where the driver is at fault.