Im not particuarly fond of your workout routine... however if thats what u want to do thats your own personal opinion.
Your soreness is most likely DOMS-delayed onset muscle soreness, this can be a result of starting a workout session, a change to a program, and or changes in form and weight. Now its a highly disagreed upon what is the actual cause of DOMS, it was originally thought to be the accumulation of lactate in the muscle itself from breakdown of glycogen, now the thought is more that its more at a cellular level cause from the constant depolarization of the muscle spindle and the sodium potassium balance. And some just think its fatigue. THAT being said, DOMS doesnt mean u cant continue with your workout program, however i find that it is extremely easier to lift heavy and stay focused without any other variables in teh way (such as soreness). If it is prolonged it may not actually be DOMS it could be a slightly more intense muscle tear, which will heal itself given some time. To solve DOMS quickly you more or less have to treat the symptoms in expectation of getting DOMS. Frequently if you have a workout and feel like "oh man im going to be sore tomorrow" well go into a hot shower, focus the water on the spots that are supposedly going to be sore and stretch for prolonged periods of time till they feel looser. Also try to sleep in a supine position.