Is it permissible to perform tayammum instead of ghusl to cleanse oneself from janabah due to embarrassment?

Your action was incorrect because a person in a state of janabah (definition) (major ritual impurity) must perform ghusl (definition) (ritual bath) as long as they are able to use water, and their state of impurity is not lifted except by that. If you performed ghusl after that, then your state of impurity has been lifted. Regarding the obligation to make up those prayers, there is a difference of opinion if you believed it was permissible to suffice with tayammum (definition) (dry ablution) in that situation. Praise Allah for His repentance, continue in His obedience, adhere to dhikr (remembrance of Allah) and du'a (supplication), associate with the righteous, and strive to learn the rulings of the Sharia (definition).