If a parent were to sue for medical malpractice on behalf of a minor, would the parent also be entitled to sue for mental anguish on behalf of themselves?

There is a million cap on medical malpractice. If a parent were to sue for medical malpractice on behalf of a minor, would the parent also be entitled to sue for mental anguish on behalf of themselves? If so, what would the statute of limitations be for the mental anguish suit, if separate? (Normally for medical malpractice, the statute of limitations is one year, but for minors it is extended because problems from birth might not be evident right away).

The reasons I am wondering if they can be two separate cases is that there are two separate plaintiffs (the child who was injured (malpractice) and the parent (mental anguish)) and in order to maximize total recovery for the family since there is the cap on medical malpractice.

I was rear ended 4 months ago. No doubt of the other guys guilt. He received 2 tickets for it and we even have the surveillance video from the store I was turning into. My question is, I received as they call it a soft tissue injury. I was taken by ambulance to the emergency room, MRIs showed the muscles affected were spasming severely. I was put on a 5 lb weight limit and pain pills and muscle relaxers. I was unable to do even routine things like sweep my floors let alone able to even pick up my children. The insurance company is not denying their responsibility but they only want to pay me 00 to cover my pain and suffering and mental anguish due to the recklessness of their client. I missed work, I have unpaid medical bills still that are currently in collections, and I still have pain if I over due it at work to this day. They are willing to pay my medical bills of 00. I have asked for ,000 to cover what I believe the pain and suffering and the total disruption to my life for the last 4 months since their client negligently hit me. They claim the 00 is their final offer, am I asking for too much? Or are they just not willing to pay what they should. I know of people who have gotten alot more for alot less happening.
It took me 3 1/2 months to decide what I have been though does equal money because I didn’t want to sound greedy. But realisticly how else to you get validation for the heartache, pain, stress, and interuption of your life? I feel by not "paying" something they are belittling the real pain, the loss of experiences, the loss of time that I missed out and can never get back because of their clients carelessness.
Thank you to those who understand what I was asking. Boo to those of you who try to judge and down grade what I am doing. 5 months ago I may have said the same thing as some of you, then I have had to go through the hell of this "accident". Don’t judge me until you have walked in my shoes. For those of you with the good advice, I have planned on settling for less without a lawyer, mainly because the guy’s insurance policy won’t pay more than ,000 so if I used a lawyer I would probably only get -6,000 anyways. I just wanted to make sure I was on the right track. Thank you!!

I am going to be receiving settlement money from a Personal Injury Mental Anguish Claim. I live in Texas. Is this taxable?
Based on the recent conflicting responses: a few more details: This is a suit made for mental damages due to sexual assault. The case is purely mental anguish/suffering. There is not a physical component.