If you travel close to C, those photons will be blue-shifted into (depending on velocity) very energetic photons (x-ray, gamma spectrum) that may be rather difficult to shield against.

But when you accelerate even more, it will be C++.

Special Relativity states that it's time that changes, not the speed of light. C is constant regardless of your reference frame. So, it's still C, but instead, it will take a lot longer to complete your project. You're definitely going to miss your deadline.

The hydrogen may be a problem well before the light or CBR become another.