I believe it's the acoustic reflex which is the natural defense mechanism of the ear to protect itself from loud sounds. I couldn't tell you whether that means you are doing damage although I am sure it would depend on the person. I also experience this but in both ears and I would say my tinnitus is probably between mild and moderate. This reflex is also known as the stapedial reflex.
As for why you don't feel it in your ear with more severe tinnitus I believe the abstract to a study I found below may hold the answer.
Abstract
Chronic tinnitus is a prevalent hearing disorder, and yet no successful treatments or objective diagnostic tests are currently available. The aim of this study was to investigate the relationship between the presence of tinnitus and the strength of the middle-ear-muscle reflex (MEMR) in humans with normal and near-normal hearing.
Clicks were used as test stimuli to obtain a wideband measure of the effect of reflex activation on ear-canal sound pressure. The reflex was elicited using a contralateral broadband noise. The results show that the reflex strength is significantly reduced in individuals with noise-induced continuous tinnitus and normal or near-normal audiometric thresholds compared with no-tinnitus controls. Due to a shallower growth of the reflex strength in the tinnitus group, the difference between the two groups increased with increasing elicitor level. No significant difference in the effect of tinnitus on the strength of the middle-ear muscle reflex was found between males and females. The weaker reflex could not be accounted for by differences in audiometric hearing thresholds between the tinnitus and control groups. Similarity between our findings in humans and the findings of a reduced middle-ear muscle reflex in noise-exposed animals suggests that noise-induced tinnitus in individuals with clinically normal hearing may be a consequence of cochlear synaptopathy, a loss of synaptic connections between inner hair cells (IHCs) in the cochlea and auditory-nerve (AN) fibers that has been termed hidden hearing loss.
Wojtczak, Magdalena et al. "Weak Middle-Ear-Muscle Reflex in Humans with Noise-Induced Tinnitus and Normal Hearing May Reflect Cochlear Synaptopathy."
eNeuro vol. 4,6 ENEURO.0363-17.2017. 27 Nov. 2017, doi:10.1523/ENEURO.0363-17.2017
I could be totally off in my thinking here so someone smarter than me like
@Matchbox should probably correct me if I am wrong but I would assume this could possibly mean the stapedial reflex in your ear with worse tinnitus might be significantly weaker than the one with the milder tinnitus which is why you aren't feeling it as much.