May I shave my shoulders and back with a razor and if not with hair removal cream?
This is permitted if the hair is disturbing. Please see sources below.
Halachah prohibits a man from beautifying himself in the manner of women, and it is therefore prohibited to shave one’s body in places that it is the way of women (and not men) to do so.
The Talmud (Nazir 59b) specifies pubic hair and armpit hair as being prohibited for men to shave. According to Rashba (Vol. 4, no. 90; see also Beis Yosef, Yoreh De’ah 181, and Bach 181:8-9), this prohibition applies to the entire body. However, the Rambam (Idolatry Chap. 12:9) writes that the prohibition (in his opinion, rabbinic) applies specifically to places that it is the custom of women alone to shave. This is also the ruling of the Rema (Yoreh De’ah 182).
Therefore, if it is generally accepted for men to remove hair in a given part of the body, it is permitted to do so. For parts of the body where it is not generally accepted for men to remove hair, it is forbidden to do so for the sake of beautification, but it is permitted to do so if one requires this for purpose of medical treatment, or other non-beautifying purposes (see Darchei Moshe, Yoreh De’ah 182, concerning shaving arm-hair for somebody who is ashamed; see also Tosafos, Shabbos 50; Iggros Moshe, Yoreh De’ah 2:61; Seridei Eish Vol. 2, no. 40 — the final two sources refer to the prohibition of coloring one’s hair, and write that it is permitted for non-beauty purposes).
Thus, although the Rashba prohibits using a razor for body hair, the common custom it to be lenient for places where it is accepted to do so.
However, it is always permitted to remove hair if this is physically disturbing or embarrassing etc.