A single INQ only hurts your score a tiny bit. Depending on your credit file, a single INQ may not hurt at all. However, it never helps your score.
If you score goes up after getting a INQ, it is due to other factors on your credit report. For example, your utilization may be slightly lower. A new account could no longer be counted as a new account. Your AAoA could increase past a year mark. Or many other possible reasons why your score could coincidently increase at the same time you also get an INQ.
