You aren't thinking clearly on this problem. Vapor pressure is, basically, a fixed property just as boiling point and density are fixed. When I say "fixed" I mean they are determined at a particular temperature or pressure.
The relationship you give for total pressure is true for ideal compounds that don't interact with each other in the liquid phase. No bonding, reactions, etc. And it presumes that the vapor space above the liquid is fully enclosed and contains only the same compounds that are in the liquid (i.e., no air).
The mixture won't have a "boiling point" in the same sense as the pure HC. As you raise the temperature, the vapor pressures increase and the equilibrium concentrations between liquid and vapor change. If the total pressure is higher than the combined vapor pressures then there will be phase transfer but it will be slow and not result in an observed "boiling" appearance. But if the total pressure is lower than the vapor pressures then there will be rapid phase transfer which is observed as "boiling".
What happens in a closed vessel as the temperature is raised? The total pressure increases.
What happens in a closed vessel with pressure control (relief valve) as the temperature is raised? You can do the calculations according to your formula - and because the VP of H2 is so much higher than the HC I think you'll find that the H2 is stripped out of the mixture first until the temperature reaches the boiling point (at the controlled pressure) of the HC, at which point you'll observe a "boiling" effect.
Having said all of that, when dealing with slightly dissolved gases in liquid, the usual relationship to use is Henry's Law.
Hope this helps!
Steve