Alice - the issue you face is not uncommon. Take along your manager or local representative when you go to collect the goods - some one who speaks the local language and can verify that the goods are yours and are only for personal use and have not been imported on behalf of any third party. Any gifts over a certain value (probably over $25 or $ 50 US) will need to be identified as these will attract import duty.
You are probably going to need proof of purchase (receipts etc), approximate dates of purchase; sign a statement that the goods are not intended for resale and probably have to sign further documents that you will take the items with you when you leave. Items with high resale value - household electrical goods, computers, cameras will probably have to been identified via serial numbers, model descriptions. I am surprised that the people you are working for did not brief you on these issues.
Hope this helps and that you have a great time in Uganda - just stay away from the NW border country.