I don't want to discourage you or anyone from applying were you to lose your primary job, but you have to report all sources of income to TWC to claim UI benefits. A side income of 35K is more than 125% of the current maximum weekly benefit amount of $465/week (see the reporting earnings link below).
If such work is occasional rather than steady, then conceivably there may be some weeks where you would qualify to receive benefits (assuming an approved claim) and others where you would not. However, that determination would ultimately be made by TWC, not a random person on the internet (me).
My personal opinion on UI is that if you lose your job due to no fault of your own, you should always apply for UI benefits. Always. The regular occurrence of that circumstance is why UI exists. I understand that many individuals are reluctant to claim government benefits of any kind, whether they have a moral opposition to it, see it as a sign of personal failure, or for whatever reason. Not taking the help that is available to you is a personal choice. But UI is there to help.
And it's not like these benefits are designed or adjudicated in any way to keep people on the couch and out of work. Applying for benefits and having an approved claim does not mean the state just mails you a check every week. There are hundreds of rules and regulations on state UI, many of which were designed to favor employers over workers. This is especially true in Texas, by far the stingiest state in the US per capita (last stat I saw was that Texas approves less than 40% of UI claims). Still, the basic premise of the program is simply to ease the burden of a sudden loss of income and help people get back to work without becoming destitute.