Since I have carried PIP (personal injury protection) insurance, won’t my insurance company have to give those funds to me to help cover all my expenses – especially since the other driver who caused the accident carried so little coverage?

In most cases they will give you those funds. However, they can refuse to pay out any of it if there’s clear proof that you were driving under the influence of either drugs or alcohol at the time of the crash. Likewise, if they can prove that you were in the process of committing a felony at the time of the accident, your insurer will use that as a valid reason for not paying out your PIP funds.