Your options are:

1) Flattening the layers and exporting your PDF.

This is not the ideal solution because of the loss of quality.

2) You can try to open your .psd files with the layers in Illustrator

See if your fonts show properly. If they do, go on the menu "Type" in Illustrator and select "create outline". Your fonts will become graphics of perfect quality. Then you can simply export your PDF from Illustrator.

See this how-to: How to convert text layers in Photoshop to vector in Illustrator

If you still get some error message after this, your problem is not related to the fonts.

Your options are:

1) Flattening the layers and exporting your PDF.

This is not the ideal solution because of the loss of quality.

2) You can try to open your .psd files with the layers in Illustrator

See if your fonts show properly. If they do, go on the menu "Type" in Illustrator and select "create outline". Your fonts will become graphics of perfect quality. Then you can simply export your PDF from Illustrator.

See this how-to: How to convert text layers in Photoshop to vector in Illustrator

If you still get some error message after this, your problem is not related to the fonts.