Agree you're definitely at fault so I wouldn't waste time arguing about liability. The other driver has every right to drive along the road and as you were joining it, it was your responsibility to ensure the road was clear before you pulled out.
As you've told your insurance, chances are her insurer will deal with the damage to her car then send their outlay (bill) to your insurers who will check it is reasonable against the info you provided, then pay it.
Your no claims will be effected because of her claim on your policy.
For your car, at 20 years old it will likely be considered a write off because your insurers will need to repair with new, manufacturer parts and they are expensive while the value of your car in comparison will be low (unless it's some sort of classic).
If you don't want it written off, call your insurer now and tell them you don't wish to claim for your damage. You can always change your mind later if you get a repair quote and it's too high but if your insurer has their garage or assessor look at your car and put a write off category on it, your insurer is obligated to add it to a database that will add a write off marker to your car and it will not be removed.
If you go ahead and claim for your damage and the car is a write off, it will likely be a category N (non structural damage) and there is nothing to say you can't keep the car. Your insurer would value the car then deduct certain costs but given the likely low value, it's probably not worth it (for example, they'll deduct your excess, the amount they'd get from the salvage company and any outstanding premium then give your whatever is left over).
I've been in your position (18yo car) and chose not to claim. Got a second hand bumper from a scrap yard (I needed front bumper and the other car has been hit hard at the back, writing it off). Mechanic fixed it for less than £200. 4 years later the car is still going fine.