Do written prescriptions expire?

[odd-boi-out.livejournal.com]

About a month ago, I went to see my doctor and she gave me a prescription so I could refill my T.  However, I still had another refill left on my old prescription, which I have since gotten filled.  So now I just have this written prescription for T sitting around in my room.  I won't actually need to fill it until May or June, but I probably won't have to see my doctor again until July or August, and I'd rather not have to make an extra/earlier appointment just to replace this prescription if I don't absolutely have to.  There is no expiration date written on it, as far as I can tell, but I'm wondering if the pharmacy will think it is too old to actually fill it for me, as it will be about 4 months old by that point.  What I really don't want to have happen is to run out of T, send the prescription in, have the pharmacy refuse to fill it, and then have to try to make an appointment with my doctor at the last minute.  And I use Stroheckers pharmacy in the US, if that matters.

Thanks!