In yoga, the practice specifically designed to boost immunity include most of the back-bends, and chest-openers. There are both simple and advanced versions of these. I have found, as an instructor, that those who have a weak immune system usually experience a mild sense of fainting when doing these chest-openers. This is rather common and not a cause for alarm. In such a case, it would be advisable to phase your practice, so that the body is slowly made accustomed to this new element. In a few weeks, this fainting sensation would go. If it persists, you need to have a thorough check-up, to establish cause and find out if you have vertigo, inner ear infection, low blood pressure or cervical spondylosis.
Another way to ease this is by using props like cushions, chair support and bolsters. This also takes some pressure off the body. The immune boosting poses work by rejuvenating the thymus, at the chest, and boosting lung capacity, thus aiding circulation. The lymphatic drainage is also facilitated, aiding faster disposal of waste. Chest-openers in yoga include the classic matsyasana (fish pose), supta vajrasana (lying thunderbolt), ushtrasana (camel), ardha chandrasana (crescent pose), bhujangasana (cobra) and all its variations.
An interesting reason why yoga works is also because bones become denser due to the resistance training that the anti-gravity poses provide. Dense bones means more production of white blood cells, needed to fight invasive infections. However, to achieve this end, you must move into the intermediate range of poses, such as the bow (dhanu), sarvangasana (shoulder-stand), santolanasana (balance pose), parvatasana (mountain), urdhava mukha svananasana (upward facing dog).
"Yogic science explains hypersensitive reactions as the arousal of a previously developed mental samskara or impression, which has left a deep-set memory and imprint in both our psyche and cellular memory (surveillance system). The person who suddenly starts sneezing either in a tense psychological situation or when exposed to house dust is manifesting essentially the same reaction. It is the physiological immune response to a subconscious mental impression surfacing": Dr Swami Karmananda in the book Yogic Management of Common Diseases, published by the Bihar School of Yoga.