How long for legs to get used to fixed gear 15 mile daily ride
First off, I assume when you say "fixie" it is a pure fixed-gear bike? It's not a flip-flop (where the wheel can accommodate a fixed cog on one side and a freewheel on the other)?

If it is a flip-flop, you'll find it easier to ride single speed rather than fixed.

Second, I agree with much of what @Arne has said in your comments. From these you say you're riding 45x15 - I think one of the beauties of fixies is that they're easy to work on, and you can easily buy cogs with more than 15 teeth. Similarly, but a bit more expensive, you can easily buy a chainring with fewer than 45 teeth. Either of these (or both of them) will make your ride easier (and therefore ease on your muscles). 

A site I like is Velosolo, not so much because they have great prices or anything (although I have bought from them and it was a good experience), but they have a good selection of single-speed/fixed-gear parts, so you can evaluate what your options are. 

But make sure you keep your current parts as you'll likely want to put them back on the bike in a month or so.