I don't think you are being selfish or greedy for wanting to make sure your DH is cared for, especially when he has an ailment that will unfortunately be with him for years to come.  I will definitely add your financial need to my prayer list.   

Greed is asking for something:

1. You don’t need
2. You want just for the sake of wanting it

Clearly, you have a need.  I believe that one of God’s preferred ways of having a relationship with us is through a sincere and rich prayer life.  So I don’t believe you should feel any discomfort in going to the Lord in prayer for things that you NEED.

But I believe I understand where your concern is coming from.  In these times of false name-it-and-claim-it prosperity theology “preachers/teachers” most sincere and good Christians tend to shy away from even the semblance of appearing “greedy” or “wanting money.”

My favorite scripture is 1 Peter 5:6-7 ~ “All of you, clothe yourselves with humility toward one another, because, "God opposes the proud but gives grace to the humble."  Humble yourselves, therefore, under God's mighty hand, that He may lift you up in due time.   Cast all your anxiety on Him because He cares for you.”

To be humble is to be empty of pride and self-sufficiency.  Often, the only way we become convinced of our own inability is for God to remove the resources and supports which we by nature depend upon.   We may lose a job, have a medical crisis, etc.  Any number of things could happen to us to send us running back into the safe protective arms of Our Father.  I call it Severe Grace.  LOL!!!

I will share with you what I personally believe and hopefully that will help you find the best way to communicate your needs to God.

I highly suggest journaling your prayers!  Find a beautiful covered book and write down your talks with God!  We ask God for so much that when He does answer prayer in HIS TIME, we tend to forget the blessing was something we asked for!  We tend to consider the blessing the work of our OWN hands, and not answered prayer from God.  If you have a written record, and watch for His Work in your life, from time to time you can go back and have the miracle of His Love revealed to you in ways our mere conscious does not allow us to grasp.

Don't ever feel inhibited because you think you cannot pray (or if you believe you should not pray for certain things).  If you can talk, you can pray!  And don't be concerned about prayer talk, church talk, or Christianese talk!  The Bible tells us the ONLY qualifications we need:

Hebrews 11:6 ~ "He who comes to Him must believe that He is, and that He is a rewarder of those who diligently seek Him..."

We just have to believe that He is a good God!  The more you pray, the more you will find to pray about, and the more you'll be led to pray for others (family members, friends, enemies, all those in authority in your life (pastor, teacher, boss, governer, president…))  You'll pray for them not only because they influence your emotional health and because part of the peace you experience will result directly from that type of praying, but because Jesus asked you to do it! 

An outline for prayer (you don't ever want to reduce prayer to a simple formula, but it is helpful to include certain key points in each prayer time...):

A.  Tell the Lord how much you love Him
B.  Thank Him for all He has done for you (list and be specific)
C.  State how dependent you are upon Him.
D.  Tell Him EVERYTHING that's in your Heart
E.  Confess anything that needs to be confessed
F.  Give Him ALL your requests
G.  Wait for Him to speak to your heart (write down what He tells you)
H.  Praise Him for working Powerfully in Your Life!

15 Reasons to Pray:
1.  To seek the face of the Lord and know Him better (Psalm 27:8)
2.  To get your eyes of your problems and onto the Lord (Psalm 121:1)
3.  To speak to God (1 Peter 3:12)
4.  To unburden your heart (Psalm 142:1-2)
5.  To make your requests known to God (Matthew 21:22)
6.  To hear God (Proverbs 8:34)
7.  To be free of suffering (James 5:13)
8.  To resist temptation (Matthew 26:41)
9.  To be rescued from distress (Psalm 107:19)
10.  To receive God's reward (Matthew 6:6)
11.  To withstand evil (Ephesians 6:13)
12.  To have joy (John 16:24)
13.  To get close to God (Isaiah 64:7)
14.  To be healed emotionally (James 5:13)
15.  To have peace (Phillipians 4: 6-7)

All that said/shared, in your situation, pray to God for what you need.  Ask that His Will be done in your life and that of your family, in whatever manifestation He deems to be Perfect.  But be prepared!  God WILL answer your prayer, but it may not come packaged and wrapped as you expect, or in the time that you expect.  If you have done everything you were required to as far as your legal and medical circumstances, and your preparation was sound, lay the rest (including the amount of the settlement) at His Feet.  Have faith that He has already taken care of you!

Jeremiah 29:11 ~ “For I know the plans I have for you," declares the LORD, "plans to prosper you and not to harm you, plans to give you hope and a future.”

Sorry for your when it should've been you're!

Jypsi, I don't think your being greedy.  My mom's neck still hurts from a car accident 40+ years ago when a telephone company van ran a stop sign and hit us.  Luckily everyone survived without serious injury.  My prayers go out to you and your family.  It's unfortunate that the drunk driver was not held accountable.

TUP & Stampman, you make excellent points.  Jypsi,  I will also pray that all of your family's needs are met and that the law suit is handled speedily.

God knows your heart and your needs!  Keep the faith!

That is a good question, can you file a civil suit?