Can nicotine gun cause my stomach to look swelled and puffy?

No. Nicotine should not have that side effect. However, if you swallow the nicotine-containing saliva, it can cause nausea and vomiting in some people. The lozenges are easier to use, and you might try those. If you are having any abdominal pain, nausea or vomiting after use of the gum, stop using it and consider nicotine skin patches instead.