Can I get rid of lacrimal glands because of bilateral swelling? (Photo)

NO! You need your lacrimal glands to make tears. You likely have prolapsed lacrimal glands. They can be tucked back into the orbit with a local anesthesia procedure as depicted in attached video. See an oculoplastics expert.

From this photo it looks like you have a prolapsed lacrimal gland.  The gland can be repositioned back up under the bone with a surgery.  See an oculoplastic surgeon to discuss this. 

The correct treatment for visible or prolapsed lacrimal glands is to resposition the back up under the superolateral orbital rim. They are there for a purpose and removing them will lead to chronic dry eyes....a far worse problem than you have now.

As noted below you should never remove a lacrimal gland as it produces your tears and keeps the eye lubricated. That being said it can be repositioned underneath the bony orbit so it is not so prominent. As noted below please see a board certified plastic or oculoplastic surgeon to discuss the option.

 You need your lacrimal gland for tear production, and it should never be removed. There is a procedure where a prominent gland can be tucked under the orbital rim so it is not so visible.