Asking "Can I...?" is asking whether you are actually capable of doing something. Asking "May I...?" asks whether you have permission to do something.
- Can I eat a pound of peanut butter [without being sick]?
- May I eat a pound of peanut butter [or should I share it]?
If you are asking "Can I use your help?" you are asking someone whether you are capable of making use of help from them. You are not asking them whether they are capable of helping you.
The answer would be "I don't know; can you use my help?" to which your response would be "Yes, I think I could."
In this situation, neither "Can I...?" nor "May I...?" are appropriate, even though both those questions are entirely grammatical, as shown in my first two examples. You're not asking about your ability to use help (you know you can, if it's offered), nor are you asking permission to use help (no-one can give you that permission but you yourself).
If you would like to ask for help, then either simply ask that, "Could you help, please?" or make a statement "I could use your help here."