Hi Jacqui, what a very sad story! I can relate a little bit as we had a day of unusual torrential rain here on Wednesday. My gutters overflowed and destroyed some potted plants I had just divided and re-potted and I was out there with an umbrella just like you, moving pots and trying to save stuff.
On the insects, the webs may be from spider mites. I would try just a simple soapy water spray first. 1/2tsp dish soap to a quart of water in a spray bottle, and spray all surfaces of the plants, especially the undersides of the leaves. Always go with the most non-toxic thing first, and soap is usually very effective. If it is web worms, (but that seems unlikely since they prefer the trees) the best solution is Bt, which you can buy as a concentrate at any nursery or big box store.
As far as delphiniums go, they are a hardy perennial, but not something well suited to your warm, humid Texas climate. Garden centers have no morals when it comes to selling you a plant that really won't do well where you are. Don't trust Wal-Mart, Lowe's or Home Depot to have good plants for your area, because they often send the same plants to Kansas and Texas and Florida with no regard for survival. Go to a good specialty nursery, and ask for tropical perennials and also native plants that have evolved to withstand the climate and the diseases and bugs that also live there.
Some of my favorites are gingers, and although they don't come in blue, there's a so-called "blue ginger" Dichorisandra that is a very easy plant. They all love lots of water and will even grow in standing water so you won't have to worry when the summer storms come along with another deluge. For the best dark purple that loves lots of water, Louisiana Iris 'Black Gamecock' is beautiful but blooms for just a short while in the spring. If you have a soggy corner, this is another one that will grow in very wet conditions. Plant them along an edge, and they'll hold your mulch from being washed away down the street next time. The best blue in my garden is a little, low-growing groundcover type plant called Blue Daze that will make a mound about 10in. tall and 2ft. wide and cover itself with little blue flowers from March through November. Oh, and of course there's plumbago - gorgeous light, bright blue flowers on a pretty, small shapely shrub.