[Edited: This answer has been improved since original posting based on comments.]
You have this backwards. If you have a 95% prediction interval, then you expect that 2.5% of future observations will have values larger than the upper limit, and 2.5% of future observations will have values smaller than the lower limit. If you don't care about values that are smaller than the lower limit, then you can just use the upper limit as the top bound of a 97.5% one-sided prediction interval, as the same percentage will exceed it whether you care about the lower bound or not. On the other hand, if you want to be able (later) to say that 95% of future observations will be below some limit, then you need to get a 90% prediction interval (and subsequently ignore the lower limit).
Note: standard equations for calculating a prediction interval following an OLS regression fit assume that the data (specifically the residuals) follow a normal distribution with mean = 0, and variance = $\sigma^2$. (This means, among other things, that the distribution is symmetrical.) This answer is assuming that as well. If your residuals are not normal, a bootstrapping approach may be appropriate. For example, you could simulate a bootstrapped distribution, sort it, and take the 95th percentile as the upper limit of a 95% prediction interval.