Restoring the limb
There are a number of methods available in D&D for removing the Petrification effect. Most are only available to mid to high level spellcasters but, if you lack access to these spells personally, you might be able to find an NPC who can cast them for you, for a reasonable fee of course. Below are a number of spells which may help alleviate your condition, their spell level is also listed for your convenience:
Dispel Magic 3rd level - If the condition is being caused by a magical effect, a casting of Dispel Magic could remove it. It automatically succeeds at dispelling a spell of equal or lower level than the slot used to cast Dispel Magic. If it is a higher level, the DC is 10 + the level of the spell. This should be your first port of call as it is one of the easiest options available.
Remove Curse 3rd level- Another easy option, this will remove the effect, no questions asked - so long as the effect is being caused by a curse.
Reincarnate 5th level - An interesting choice as it requires someone to kill you, and spend 1000 gp. Effectively, someone would kill you, cast Reincarnate on you and the spell would magically create you a new body. You would be able to keep all your experience and memories, but you might change race unless the DM allows you to stay as the race you are currently.
Greater Restoration, 5th level - This spell specifically states it will remove petrification and thusly allow for the use of your hand.
Regenerate, 7th level - Cutting of your hand and then casting Regenerate would certainly solve your issue. Your hand would grow back within a couple of minutes. However, this is a 7th level spell which may be too far out of reach for your party.
Resurrection, 7th level - Similarly, Resurrection would restore your limb if it was cut off. Again though, this requires you to die and 1000 gp to be spent to cast this spell. You would also suffer some temporary side effects.
Clone, 8th level - You could create a clone of yourself, die, and then come back into your own body with your hand now working.
True Polymorph, 9th level - You could polymorph into yourself but with a functioning hand.
True Resurection, 9th level - Once more, you are required to die and have your hand chopped off, but this would work.
Wish, 9th level - Wish, the mightiest spell available. It would be a simple task for wish to restore your hand to flesh and blood, but it is not recommended. There is a 1/3 chance that you would never be able to cast the spell again after using the Wish spell in this way. It is simply not worth the risk when there are better alternatives. You could however use Wish to duplicate the effects of an 8th level or lower spell, one which would restore your limb or remove the petrification, without costing material or costly components.
Working around the issue
Whilst the above list of spells will give you a way to resolve your problem permanently, there are other solutions which, in my opinion, are far more interesting. Notably, the cantrip Mage Hand.
I think it would be really interesting to see a character who has lost the ability to use their physical hand use magic to replace its function. Whilst everyone else is using it for manipulating objects at long range, this character is simply using it as almost a prosthetic hand, to do the things they might otherwise struggle with. You could also cast Unseen Servant to perform menial tasks for you like cooking, cleaning, repairing etc.
Prosthetics from Eberron: Rising from the Last War could also help to solve your issue, though you’d have to find a way to get your hands on one of them. They are common in the world of Eberron but you may be hard pressed to find one in the Forgotten Realms. With the DM’s discretion, you may be able to find an NPC who can craft you such a limb.