Radioactivity should not matter. Break the sample into smaller parts.

I agree with the answer given by Joseph L Alvarez. If you wish to confirm that it is radioactive and enriched in uranium and or thorium then quite a number of measurements could be undertaken both in the area of study using a Geiger-Muller Counter or in the Laboratory with Scintillation and HPGe detectors. Mineral identification can be done using XRD, EPMA etc. apart from looking at their thin sections (or may be polished sections)under a suitable microscope. Though the radioactive minerals are generally 'opaque' but you could see some halos or micro-fractures/deformation due to 'radiation damage'. All the best for your future studies.

In addition you could use the thin sections/polished section of minerals/rocks using EPMA or any other related facility. These are most suited and extensively used for identification of radioactive minerals and whether comprise of primary or secondary uranium and/or thorium enriched minerals.

Usually Allanite minerals are not highly radioactive. Thorium and Uranium, in amounts up to 5 ThO2 and 0.5 U3O8 wt.% respectively, are present in the majority of Allanites. These natural radioisotopes are easily measured my ICPMS. The crack or damage in mineral is may be due to the alpha particle irradiation present in mineral.