How long do I have to fix my car after I get the insurance check?

Start with what is actually written down. The rules we can quote put clocks on the company. It must tell you it got your claim within 15 days of getting notice [1]. Once it holds every item it asked you for, it must accept or reject the claim in writing within 15 business days [2]. If it says it will pay, it must pay within 5 business days of that notice [3].

Now your side. No page quoted here gives you a number of days to repair the car after the payment arrives, so this answer prints none. What binds you sits in two other places. One is your own policy. The other is your loan or lease. TDI says that if you still owe money on your car, your lender will require you to have collision and comprehensive coverage [4]. The pages quoted here say nothing else about a lender's terms.

Two things the sources do settle. The company bases its payment on the adjuster's estimate, and if the damage turns out to be worse than the adjuster first thought, you or the repair shop can talk to the adjuster about raising the estimate [1]. And the payment has a ceiling: the company pays for repair or replacement only up to the car's actual cash value, which is the cost to replace the car minus depreciation [5].

What the sources do not give: a deadline for you to repair, whether you may keep the money and leave the damage, and how the company treats the same damage in a later claim. Don't know yet. The lender is the one that requires the collision and comprehensive cover [4].

Read the «Auto claims» and «Settling claims» parts of the TDI auto guide at the links quoted here, then read Tex. Ins. Code §542.056 and §542.057.