I beg to differ. I think what Michael and Chris are saying is that they can't figure out how having this "two hashtag" information would be particularly useful. And I confess, I find myself in that camp as well.
Interesting, yes. Fun to play around with, of course. But I'm having a hard time visualizing what information I'd get from it that I wouldn't either already know or be able to find out easily enough through other channels. But you're not telling us what you really want to do with this information; you're simply asking specifically about what services might let you search two hashtags simultaneously.
So when you ask for a tool that will let you look at two hashtags at once, well, the only one I know of off the top of my head is hashtags.org (and the only reason I know about that one is because you mentioned it). But you've already said you don't want to pay $49 a month for their service. Now, thinking logically, if you can gain more than $49 worth of additional business from having this info, then refusing to pay $49 a month is silly. You'd recoup the money almost immediately, and then some. So, what you're saying is that you think being able to simultaneously search on two hashtags is going to bring you somewhere between $0 and $49 of additional business per month.
Which again begs the question: why bother? So, we must be missing something.
If we knew what you were trying to accomplish -- not "search multiple hashtags at once" but whatever it is you think you're going to be able to do with this data -- we might be able to suggest an alternative means of getting the information you need. Our experience over many years here has been that people often think they know what they "need" and come in here asking for that... but what they really need is something else entirely. It turns out they've misunderstood a "tip" they read somewhere, or that they have a misguided idea about How Things Work, or that they've fallen for the sales hype of some service provider, or they're simply not that experienced with marketing in general.
Not saying any of those are the case with you, of course. But it's easier for us to provide useful answers if we know what the actual goal is.