At the time you will be here, there will be plenty of birding sites in and around the Houston area. I would definitely *not* head south as recommended by your UK birding friend. So many that your days will be full enough in the Houston area to where you really have no need to go to the southern part of Texas. And too, the southern part of TX can already be pretty warm by mid-April. Why waste a full day of driving anyway?
In upper TX coastal area, you have many small places within the Houston metro area to bird. But within a 100 mile radius of H-town, you have:
Anahuac National Wildlife Refuge
Brazos Bend State Park
Sea Rim State Park
Sabine Pass State Park
Galveston Island State Park
and a whole host of other smaller places too numerous to mention. Slightly further away is Port Aransas/Rockport/Aransas Pass/Goose Island area, although I think the whooping cranes will already be gone.
Don't get me wrong -- south TX is a fantastic place to bird. However, you will be extremely close to some world-class birding areas at the right time to make it worthwhile, so why even go to the trouble of driving eight hours (one way) to get to S. TX?
If you get time, do some reading on the Texas Ornithological Society and the Houston Audubon Society. You will find plenty of places to bird. I couldn't recommend High Island/Sabine Woods/Anahuac Reserve more highly...........