I am sorry to hear about this concern for Mike.
My primary concerns for a limp on a front leg/paw include:
1. Having stepped on something that no longer remains.
2. Hypersensitivity reaction (i.e. insect bite or sting)
3. Hyperextension injury (like bending your wrist back too far)
4. A soft tissue injury (like sprain or straining your wrist or ankle)
5. Fracture, especially in the digits of the paw
6. In older pets, I always think about exacerbating arthritis (common for the elbow)
So, first, I woiuld double check the nails for any fractures and the paw (paw pads) to ensure no torn pads or anything stuck in the paw.
Second, it clearly sounds like Mike is uncomfortable, so you will need to get in to a vet. I would advise against a wait and see approach. Why? Well, a vet can easily prescribe some pain medication and likely a non-steroidal anti-inflammatory to get him comfortable, regardless of the cause.
Tough to say if x-rays are indicated. It will depend a lot on the examination, and if there are any areas of increased sensitivity or any specific pain on testing range of motion in the joints (especially the shoulder and elbow).
I would advise against giving anything over-the-counter, since most are not that effective and can be hard on the stomach.
Definitely, rest and confinement until that vet visit. No going outside offleash running around.
Hope that information helps.