Is it alright to ski if I am overcoming tibialis anterior tendonitis and just sprained my ankle today?

Fine once recovered. I recommend obtaining medical clearance from at least your physical therapist and your treating physician. Ski boots tend to put considerable pressure directly over the area of your foot and ankle that is home to your tibialis anetrior tendon. Skiing is a great sport, but chronic tendinitis may diminish the fun due to pain. Swelling around your ankle will potentially make boot fitting difficult.
Bad Idea. In general one should wait until a sprain has healed before engaging in sports. And the muscle forces associated with skiing may aggravate your tendinitis. You should wait until you have recovered from both problems and have been rehabilitated before returning to spots.