I have an embroidery machine, so I embroidered my youth group's logo on to a sweatshirt. When I wore it there they said they copyrighted the logo and I should stop wearing it, because then people might want it. I don't want to stop wearing it, but I also don't want to get sued. I'm pretty sure that if I'm not making money, they can't do anything. Is that correct?
Under US copyright law, a logo that is anything more than a very simple geometric pattern is protected by copyright automatically as soon as it is "fixed in a tangible form". This means when it is written down, or saved to a computer file, or some other physical record is made of it. There is no need for anyone to take action to copyright it.
Under 17 USC 106 the rights of the copyright owner include:
... the exclusive rights to do and to authorize any of the following:
(1) to reproduce the copyrighted work in copies or phonorecords;
(2) to prepare derivative works based upon the copyrighted work;
(3) to distribute copies or phonorecords of the copyrighted work to the public by sale or other transfer of ownership, or by rental, lease, or lending; ...
By making the sweatshirt without permission, you almost certainly violated either (1) or (2) above. If you were to make copies and give or sell them to others, without permission, you would violate (3).
It does not appear that you made any profits, or in any way harmed any market for the logo or clothing carrying the logo. Thus (if I am correct) there would be no actual damages even if the group sued you and won. What there could be is statutory damages. This is money awarded because the rights were violated, regardless of the amount of actual monetary damage done. This is provided for under 17 USC 504 subsection (c). The court has wide discretion on how much to award in such a case. It can be as little as $750, or as little as $200, if the infringer did not know and did not have reason to know that what was done was infringement. The amount of statutory damages can be as much as $30,000, or up to $150,000 if the act was done "willfully".
In the situation described in the question, the lower end of that range seems more likely, but that is up to the judgement of the court. Also, under 17 USC 412 statutory damages are not available unless the copyright was registered before the infringement occurred, or within three months after the work was first published, or, for an unpublished work, within 1 month after the owner learned of the infringement.
All of this means that a copyright suit for a small, non-commercial infringement such as is described in the question, a suite is quite likely to cost more than the damages obtained. As the answer by ohwilleke says, such suits are "unlikely, uneconomical, and bad press", but the copyright holder can choose to bring such a suit, and might well win some damages.
Perhaps you and the group could agree on a license fee for permission to make and wear the sweatshirt? Then it wouldn't be infringement, and the group would get some money. Perhaps, if they think others might also want such shirts, a further deal could be made where you make and sell such shorts with permission for those who want them, and pay the group a percentage, or a per-short fee, or an amount decided in some other way. Of course they don't have to agree to any such deal, but it could be a win/win arrangement. Many groups like to have members wearing clothing with their logo on it.