First, you don't start a solo with everything you have. When you play, you build to a climax (usually on the five chord), so early in the piece, you hold back some, so you have something to build up to. There's also no reason to play too loudly, especially if you are amplified. You have much more control of your tone by playing softly.
Start your solo with enough air, but not too much air, but how much air exactly will vary with playing style. I start my solos with my lungs about a quarter full. You will need to have plenty of room to draw in air for a series of draw notes, but full enough so you have air to blow the initial blow notes. If I am playing 1st position (straight harp), where the accent is on the blow notes, I do just the opposite and start with my lungs about three-quarters full.
One problem many beginners have is the infernal leaky nose. Often, players draw in air through there nose and, unless you are also playing a harmonica with your nose, they are wasting lung capacity.
Know how to conserve air beforehand. One problem many beginners have is the infernal leaky nose. Often, players draw in air through there nose and, unless you are also playing a harmonica with your nose, they are wasting lung capacity.
Draw on the harmonica, then exhale and draw again, but this time pinch your nose with a thumb and forefinger, with just enough pressure to cut off any air flow. If you notice any difference, you've got a leaky nose and you need to work on inhaling through your mouth only.
On the reverse side, you can use your nose to dump unwanted air. It may take months for you to master this, but if your lungs are too full, you can exhale some through your nose to make some room.
Learning when not to play is as important as learning when to play. The solo is your opportunity to express yourself, you are the center of the action, but remember at other times, you are supporting someone else, whether a vocalist or another soloist. At those times, it's not about you sounding good, but you playing the right, subtle things that make them sound good.
See my article on playing harmonica rhythm for more.