I will assume your hydrangea is also a mophead but most of my comments would apply to other types of hydrangeas.... Although even greenhouse florist hydrangea leaves can be very sun sensitive, sunscorch is not something that you should be experiencing with a hydrangea in March. The sun in your NC location is just not "strong" enough yet to cause sunburn damage to leaves. For example, my sun, which is much stronger in the summer months, is not yet causing any issues to an un-planted mophead hydrangea that I have getting morning aaaaand afternoon sun (10+ hrs of sun) so it is shocking that your shrub is having that type of problem. Also, sun damage should only affect those leaves in direct contact with the sun by turning the leaves yellow-ish to white-ish; any inside/inner leaves should remain dark green.
Temperatures below freezing however do sound like the culprit of dead leaves. And blooms. To prevent that, I tend to plant hydrangeas about two weeks after my average date of last frost. You live near one my sisters-in-law in Greenville and she confirms that there was cold weather on the 2nd/3rd week of this month (20s). There was: a low of 28F last Thursday; a low of 29F the week you planted (5th, 6th and 9th of March) the shrub. Your avge date of last frost is April 1st so there is still risk for this same issue to happen yet again.
It is very likely that the water in the leaves' veins froze into crystals, the veins fractured and the leaves died. Strange that damage was limited to one side but not unheard of. Sometimes the whole plant is affected. Sometimes only the top is the only affected part. The zapped leaves sometimes turn very dark green, almost blackish, eventually brown. The same type of damage could also have occurred to the stems, in which case the stem will dry out and not leaf out.
If the stems are ok, they will leaf out again although not pronto. Give them time to re-gen another set of leaves. If there are no leaves forthcoming by the end of May, you can assume that any dried out/dead looking stems will not leaf out ever and then you can cut them to the ground.
Getting leaves zapped is not fatal... the shrub is not dying and should recover, all things being equal: this problem should not have impacted the roots.
In the future, I suggest making sure that you (1) deeply water the shrub the night before temps go down or frost/freezes are announced, (2) winter protect by covering the shrub with mulch in a chicken wire enclosure (you normally want to do this in the Fall if the plant only blooms on old wood; not practical to do this year), (3) use frost cloth for small and brief dips below freezing, etc. and (4) maintain the shrub well mulched (2-4" of organic mulch up to the drip line).
There are also some vermin that will eat plant roots (voles) -hydrangeas included- and that could also result in leaves in one section of the shrub browning out. And in case s ooo m e of the browned out leaves are due to insufficient water when you were watering, I will list a few hints in that department next.
Like I said earlier, watering deeply on the prev night before the temp dip usually helps a lot... but your plant does not yet have a very good root system to absorb a lot of water asap when needed... it will next year hopefully. Again, try to water deeply not often. But give the shrub some slack on its first summer when it can be "temperamental". ;o) Ha! In future summers, the shrub will not be as bad. It depends on how quickly it becomes established in your garden.
Regarding waterings, start with 1 gallon of water per watering per plant from the crown outwards. Water the soil early in the mornings, never the leaves if you can help it (helps prevent powdery mildew leaf infections). If the soil is already moist or wet then... no need to water again. Use around 1g of water in Spring per watering. Water when a finger inserted to a depth of 4" feels dry or feels almost dry. Increase the amt of water from 1g when your temps regularly go into the 90s around July. Reduce that back when temps moderate. Reduce further to one watering per week or every two weeks in winter if winter is dry. If winter is rainy/snowy then you may not need to water hardly at all. Obviously, never water is the soil has frozen.
You can cut the dried out blooms and leaves now if they look ugly. They will not recover. If your shrub is a re-bloomer hydrangea, you will get new blooms from them in the summer/fall months (all things being equal).
Does that help?