It is customary in a post such as this to include the caliber that you are loading for and the weight of the bullet as well as the weight of the powder. From the context, I assume you're talking about 38 Special with 158 grain bullets.

As you noted, the Speer manual you are relying upon shows a range of 3.5 to 3.9 grains, so 3.7 is within that range. For comparison, Hornady #8 shows 3.7 as maximum behind a 158 grain lead bullet.

But I want to point out that proper load development dictates that when a component is changed, the loader should retreat to the starting load and work up from there. In this case, you did not do that.

If you had worked up to 3.7 grains from a lower figure that was working fine, I would probably counsel you to go ahead and shoot these loads. But, since you're starting with 3.7 grains which is maximum for Hornady and mid-range for +p loads in Speer, my advice is to pull the bullets, salvage the components and re-start the process from the starting load.