First, you might want to have a tech run an exhaust gas test to verify that the mixture is right.
THen, you'd want to review the installation instructions. Those typically give specs on what is acceptable for routing of the exhaust, the lengths, position of the outlet, the required slope, etc. One thing that is also usually spelled out in the installation instructions is the minimum clearance from openings like doors, windows, or other intakes or exhausts. If you have a window directly above, that may conflict with the installation instructions, and you'd have a case against the installer to fix it on his dime rather than yours. That sort of thing SHOULD have been caught in the inspection, but people don't always pull a permit, either, and not all inspectors are actually inspecting to the appliance's requirements, but those generally require installation to the manufacturer's instructions in addition to any 'normal' code requirements.
Running it up the wall outside probably isn't a good idea. Finding a path inside to run it up might be possible if the overall length is allowable. The condensate can freeze if you don't follow the instructions, and I found out the installer didn't on mine on a really cold day when the boiler shut down because it couldn't get any combustion air as it became blocked by the installer not following instructions. They fixed it for free, but I caught it after researching what happened and why, not them that should have been able to follow instructions (that's what you pay them for!).
So, can't give a definitive answer without the specs, and the exact location and distances of the piping involved. On some, depending on the distance, longer ones may require a larger diameter pipe, and that can make finding a path harder. The maximum distance is referred to as the effective length. That takes into account the linear measurement, but adds effective length for any changes in direction. For example, a right-angle fitting might be 1' in real length, but it might add 5' of effective length to the distance because of how it restricts the airflow. Those numbers are just for illustration, not exact...the documentation will assign the values you'd need to do the calculation. The fan and gas volumes involved will determine how much restriction the burner can work with.