Are chin ups and push ups ok to do if i have sciatica due to bulging disc n degenrative disc in the lumbar region?

If done properly: If you have a strong core, either from prior to the herniation or that has been developed afterwards, you should be able to do those two exercises. In a push up, which actually works your core, you keep your back perfectly straight if done properly. The same is true of a pull up which should utilize upper body strenght but keep low back straight. Confirm your form is correct prior to starting.

OK with Technique: Exercis is always good even with slight injury to help heal faster, however you must take caution with the use of proper technique. Prolonged extension and flexion of the spine can make things worse. Use the rule of thumb if it hurts afterwards don't do that again until you are feeling better.