I had a dental deep cleaning in the right side of my mouth and now that side its swollen and i can't open my mouth normal dic said touched a vein maybe?

Probably not: The need for your deep cleaning most likely came about due to pocketing and/or calculus build up. Your gingival tissues were already inflamed. It's possible the swelling is due to a minor infection... The lockjaw could be from keeping your mouth open a long time during the procedure. Call your dentist, you will need to be seen and you may need an antibiotic.

What happened?: My sense is that you probably had an injection for the deep cleaning, the injection for the lower teeth sometimes causes the muscle to spasm resulting in the difficulty in opening. Another possibility is that there was some internal bleeding due to the needle puncturing a blood vessel. This can cause a hematoma which would produce the same effect. Extended visit opening wide can affect jaw joints.