I know you are anxious, but unless a delay in repairs would cause additional damage or endanger persons in the area it is reasonable to give the responsible people a few days to respond. If you are concerned that you are being ignored, it could help to send a letter to the company to remind them of the damage their workers did and their promse to respond and resolve the problem. If this does end up in court, you may be required to show that you had made a written demand before filing.
Be careful what you say, even though this is not a criminal matter what you say may be used against you. Likewise, what the responsible company and their employees and representatives say may be used against them if this ever went to court. Make notes of what is said either during conversations or as soon after as possible in order to create a contemporaneous record.
Depending on the cost of repairs, in some places it is possible to hire an attorney and require the defendant in a court case to pay attorney fees and expenses in addition to your damages. That assumes you win the case, and the responsible party actually pays.
Have you contacted people for repair estimates? You want to know what it will cost to do the repairs in case you are offered some amount of money and accept the offer only to find out later that it will cost more. And you do not want someone from the tree removal company doing the repairs, you want someone with appropriate skills. If you think that you could do the repair yourself and pocket the amount of payment that would have gone for labor, you might pick up a few dollars.
It is possible, perhaps likely, that the company that did the removal is licensed by the state, and the state may have information on the company's liability insurance company. You might file a claim with that insurance company.