I would think that your best bet is to find a used vtec engine and replace the whole thing.

Here is the problem with just replacing the head. First, you will need to find the head. You might be able to find a decent used one for 2-400 bucks. But even then, you're still going to have to have the head worked. It will need to be milled (resurfaced), and pressure checked to make sure there are no cracks. In addition, if it has alot of miles, it will be recommended to have a valve job as well. All in all, you're looking at over 600 bucks, which is what it might cost you to buy a re-furbished one. If you have the head all ready, an experienced mechanic can probably replace it in 5-10 hours if they don't run into any problems. Plus, you will need an upper gasket set. My guess is over $1000 easy to have it done. Here is where it gets complicated. The bottom half of your engine is old and worn, and the top half is good. When this happens, the added pressure, (from the new head not being worn anymore), will cause more pressure on your rings. If you're rings are old and worn, (which on a 91 integra they probably are), then the increase in pressure will cause them to leak more and you will probably burn alot more oil. I've heard as much as half a quart every 400 miles. What you COULD do, is while the head is off, drop the oilpan, and remove the rod caps. Take the pistons out, rehone the cylinder, and replace the rings and rod bearings. Now your looking at more money, and you've practically rebuilt the entire engine, and spent probably well over $1500 bucks and you still have a problem with over-reving the block.

The alternative I mentioned earlier - find a decent used vtec engine with low miles. Might be able to for around $1000, then pay to have it swapped. It might cost just as much, or even cheaper, but now you have a good engine all around with low miles. Do you see the benefit?