I got into an accident two months ago with a driver who was insured by GEICO. I got a call from them yesterday saying there was no way to prove who was at fault and that they are denying my claim and their policy holders claim. Is there anything else I can legally do? I need my car fixed! Also, the lady that hit me did have an attorney and now I'm afraid she will come after me!
Texas is a little unusual because it is not a no-fault car insurance state. However, if you have paid for insurance it appears that your insurer is required to pay for your insured damages if it can't attribute and recover the costs from other involved parties.
There no point in suing the other insurer: they have done you no wrong. You have to go after the person driving the other car and sue them. Your insurance company won't do that for you, since you didn't get comprehensive that creates an obligation for them to trot out a battalion of suits to press your case. If you actually prevail in court (prove that it is actually her fault) they will pay their client. The other insurance company may feel (say) that there's no way to prove who is responsible, but if the facts are on your side, you might persuade a court. And you're right, there is always the chance that they could likewise try to prove that you are at fault (which is where your liability insurance becomes very handy).
if your insurer is denying liability but you believe you weren't at fault, you should consult a Texas personal injury attorney. He or she will be able to sit down with you, go over the facts and determine whether you were actually liable for the accident. Make sure to keep a file or Excel sheet of all expenses you've paid since the accident; this way, your attorney can try to get them reimbursed by your insurance company, should you be successful with your lawsuit.
This will also help protect your interests in the event that the other woman's attorney pursues you. A lawyer will make sure that you aren't blindsided by a lawsuit and will negotiate with the other side when necessary. Additionally, he will be able to negotiate bills with your insurance company and try to lower them if possible.
If you think that your insurance company is acting in bad faith (IE, they're unreasonably denying your claim), then you'll want to notify the Texas Department of Insurance. They can investigate the claim and, if they find that your insurance adjuster was indeed acting in bad faith, they can levy fines.
Either way, filing a claim against your insurer (and using an attorney to do it) is the surest way forward in terms of recovering a settlement and being compensated for your injuries. The insurer has a duty to investigate your claim, explain why it isn't pursuing it, and promptly issue that denial.